The most famous ladder in the Bible is Jacob's ladder in Genesis 28 (here quoted from the New King James Version):
Now Jacob went out from Beersheba and went toward Haran.
So he came to a certain place and stayed there all night, because the sun had set. And he took one of the stones of that place and put it at his head, and he lay down in that place to sleep.
Then he dreamed, and behold, a ladder was set up on the earth, and its top reached to heaven; and there the angels of God were ascending and descending on it.
And behold, the Lord stood above it and said: “I am the Lord God of Abraham your father and the God of Isaac; the land on which you lie I will give to you and your descendants.
The poem later also mentions dreaming, just like the above passage about Jacob.
However, even without this passage from Genesis, it would be possible to interpret the ladder as a symbol of a longing for transcendence. Ironically, the poet's gaze is not upwards but towards things such as "a barrel", "the drinking trough", "hoary grass" and "he cellar bin", and he mentions that the apple-picking made him tired. In spite of the longing for transcendence, physical things and physical exertion bring him down to earth.