You definitely missed something. The narrator, Bilbo, other hobbits, Gandalf and the dwarfs all have different opinions of Bilbo's propensity to burglary.
The Hobbit starts out as a children's tale which evolves into a larger fantasy novel. This shows in the structure of the novel, and reflects the history of the work. In a 1955 letter to W.H. Auden, Tolkien relates the genesis of The Hobbit:
All I remember about the start of The Hobbit is sitting correcting School Certificate papers in the everlasting weariness of that annual task forced on impecunious academics with children. On a blank leaf I scrawled: 'In a hole in the ground there lived a hobbit.' I did not and do not know why. I did nothing about it, for a long time, and for some years I got no further than the production of Thror's Map. But it became The Hobbit in the early 1930s, and was eventually published not because of my own children's enthusiasm (though they liked it well enough42), but because I lent it to the then Rev. Mother of Cherwell Edge when she had flu, and it was seen by a former student who was at that time in the office of Allen and Unwin. It was I believe tried out on Rayner Unwin; but for whom when grown up I think I should never have got the Trilogy published.
42 Not any better I think than The Marvellous Land of Snergs, Wyke-
Smith, Ernest Benn 1927. Seeing the date, I should say that this was probably an unconscious source-book for the Hobbits, not of anything else.
Children's tale or fantasy novel, The Hobbit has a reliable narrator. The narrator does choose to withhold information information and is not necessarily omniscient, much in the way that fairy tales often leave out some information, such as “[the villain] ran away and was never seen again”, to make it plausible that the narrator was a first-hand witness, but the narrator does not outright lie. (More on this, somewhat spoily, at the very end of this answer.)
The very first thing we learn about hobbits, in the opening paragraph, is that they are creatures of comfort.
In a hole in the ground there lived a hobbit. Not a nasty, dirty, wet hole, filled with the ends of worms and an oozy smell, nor yet a dry, bare, sandy hole with nothing in it to sit down on or to eat: it was a hobbit-hole, and that means comfort.
As for Bilbo himself, the narrator tells us that he is quite an honest, upstanding citizen. But if you read the third and fourth paragraph closely, you'll notice that Bilbo comes from a boring, respectable family, but he himself isn't exactly described as respectable:
This hobbit was a very well-to-do hobbit, and his name was Baggins. The Bagginses had lived in the neighbourhood of The Hill for time out of mind, and people considered them very respectable, not only because most of them were rich, but also because they never had any adventures or did anything unexpected: you could tell what a Baggins would say on any question without the bother of asking him. This is a story of how a Baggins had an adventure, found himself doing and saying things altogether unexpected. He may have lost the neighbours' respect, but he gained-well, you will see whether he gained anything in the end.
(…) the mother of this hobbit - of Bilbo Baggins, that is - was the fabulous Belladonna Took, (…) once in a while members of the Took-clan would go and have adventures. They discreetly disappeared, and the family hushed it up; but the fact remained that the Tooks were not as respectable as the Bagginses, though they were undoubtedly richer. Not that Belladonna Took ever had any adventures after she became Mrs. Bungo Baggins. (…) Still it is probable that Bilbo, her only son, although he looked and behaved exactly like a second edition of his solid and comfortable father, got something a bit queer in his makeup from the Took side, something that only waited for a chance to come out. The chance never arrived, until Bilbo Baggins was grown up, being about fifty years old or so, and living in the beautiful hobbit-hole built by his father, which I have just described for you, until he had in fact apparently settled down immovably.
Note how the narrator states that Bilbo's family was considered respectable, but not that Bilbo himself was, except by inference from his father's family. And the narrator states that Bilbo has a hidden adventurous streak that, until the events of the book, had never manifested himself.
Gandalf knows, or thinks, differently. Gandalf is a mysterious character who knows a lot. He is a wandering wizard and evidently more long-lived than normal people (even hobbits, for whom “fifty years old or so” is a young adult).
Gandalf! If you had heard only a quarter of what I have heard about him, and I have only heard very little of all there is to hear, you would be prepared for any sort I of
remarkable tale. Tales and adventures sprouted up all over the place wherever he went, in the most extraordinary fashion. He had not been down that way under The Hill for ages and ages, not since his friend the Old Took died, in fact, and the hobbits had almost forgotten what he looked like. He had been away over The Hill and across The Water on business of his own since they were all small hobbit-boys and hobbit-girls.
Such a mysterious and impressive figure may well know something about Bilbo that Bilbo himself doesn't realize. Certainly, when Gandalf first broaches the subject of
adventure, Bilbo is shocked by the idea. We don't know his exact thought process, so we don't know whether he is consciously or subconsciously tempted, but outwardly he is not at all tempted.
“(…) I am looking for someone to share in an adventure that I am arranging, and it's very difficult to find anyone.”
“I should think so — in these parts! We are plain quiet folk and have no use for adventures. Nasty disturbing uncomfortable things! Make you late for dinner! I can't think what anybody sees in them,” said our Mr. Baggins
The first occurrence of the word “burglar” in the book is in dialog from a dwarf, and we learn that it was Gandalf who described Bilbo as a burglar to the dwarfs.
This is what he heard, Gloin speaking: “Humph! (…). It is all very well for Gandalf to talk about this hobbit being fierce, but (…) I think it sounded more like
fright than excitement! In fact, if it had not been for the sign on the door, I should have been sure we had come to the wrong house. As soon as I clapped eyes on the little fellow bobbing and puffing on the mat, I had my doubts. He looks more like a grocer than a burglar!”
At this point, Bilbo's adventurous side erupts, but even still he does not endorse the appellation “burglar”.
Then Mr. Baggins turned the handle and went in. The Took side had won. He suddenly felt he would go without bed and breakfast to be thought fierce. (…)
“Pardon me,” he said, “if I have overheard words that you were saying. I don't pretend to understand what you are talking about, or your reference to burglars, but I think I am right in believing” (this is what he called being on his dignity) “that you think I am no good. I will show you. I have no signs on my door — it was painted a week ago —, and I am quite sure you have come to the wrong house. As soon as I saw your funny faces on the door-step, I had my doubts. But treat it as the right one. Tell me what you want done, and I will try it, if I have to walk from here to the East of East and fight the wild Were-worms in the Last Desert. (…)”
Note how he might talk of fighting “wild Were-worms”, but in his mind the worst aspect of adventure he can imagine is to ”go without bed and breakfast“.
After some discussion, the wise, oracular figure (Gandalf) states:
“If I say he is a Burglar, a Burglar he is, or will be when the time comes. There is a lot more in him than you guess, and a deal more than he has any idea of himself.”
So no, Bilbo is not a skilled burglar, and he does not think of himself as suited for burglary in any way. If he has any predisposition for burglary, it's his nature as a hobbit. Hobbits are good at going about unnoticed. They're more inclined to sneaking away than to sneaking in, but they're good at sneaking.
I suppose hobbits need some description nowadays, since they have become rare and shy
of the Big People, as they call us. They are (or were) a little people, about half our height, and smaller than the bearded Dwarves. Hobbits have no beards. There is little or no magic about them, except the ordinary everyday sort which helps them to disappear quietly and quickly when large stupid folk like you and me come blundering along, making a noise like elephants which they can hear a mile off.
(The rest of this answer may be mildly spoily for The Hobbit, The Lord of the Rings and other works set in the same universe.)
Regarding the differences in how much harder the start of the journey is in The Lord of the Rings compared to The Hobbit, there are several reasons. There are multiple in-story reasons which are enough explanations in themselves.
One reason is that in The Lord of the Rings, there are villains actively hunting the party, whereas in The Hobbit, the only dangers are the ones encountered on the road. This forces the party in The Lord of the Rings to go off-road. Another reason is that in the decades between the two books, evil has spread around the world and the world is a more dangerous place than it used to.
In addition, there are out-of story reasons.
The Hobbit was originally not set in the same universe of The Lord of the Rings. In fact, at the time Tolkien wrote The Hobbit, the LOTR universe as we know it now was very different: Middle-earth was only what later became known as the First Age. The Lord of the Rings was Tolkien's effort to tie The Hobbit to the world he loved and make a marketable book out of it.
Not only is there a difference of tone between The Hobbit and The Lord of the Rings — the latter book is more serious, more “adulty” — but
The story in The Lord of the Rings doesn't perfectly match the story in The Hobbit. The narrator in The Hobbit is reliable within the context of The Hobbit itself, but not in the context of Tolkien's legendarium as a whole. In fact, in The Lord of the Rings, we learn that the tale that Bilbo told of his adventures wasn't the truth. That tale was the original edition of The Hobbit, but what actually happened was the later editions of the book, tweaked to fit LOTR better. See 1 2 3