When did the bacteriologist take the cab in the Wells short story "The Stolen Bacillus"? First he was running towards him, and then near the end we come to know that he is in a cab. Is it that him taking the cab isn't shown?
Yes, the bacteriologist must have got in a cab "offstage".
Our first look at the scene in the street is from the point of view of Minnie, the bacteriologist's wife. Initially, the anarchist is in a cab, being pursued by the bacteriologist on foot, who in turn is pursued by Minnie in another cab:
Minnie, hearing the door slam violently, ran in alarm to the window. Down the street a slender man was getting into a cab. The Bacteriologist, hatless, and in his carpet slippers, was running and gesticulating wildly towards this group. One slipper came off, but he did not wait for it. 'He has gone mad!' said Minnie; 'it's that horrid science of his'; and, opening the window, would have called after him. The slender man, suddenly glancing round, seemed struck with the same idea of mental disorder. He pointed to the Bacteriologist, said something to the cabman, the apron of the cab slammed, the whip swished, the horse's feet clattered, and in a moment the cab, Bacteriologist hotly in pursuit, had receded up the vista of the roadway and disappeared round the corner.
[...] She hastily put her bonnet on, seized his shoes, went into the hall, took down his hat and light overcoat from the pegs, emerged upon the doorstep, and hailed a cab that opportunely crawled by. 'Drive me up the road and round Havelock Crescent, and see if we can find a gentleman running about in a velveteen coat and no hat.'
'Velveteen coat, ma'am, and no 'at. Very good, ma'am.' And the cabman whipped up at once in the most matter-of-fact way, as if he drove to this address every day in his life.
"Some few minutes later", we see the scene from the point of view of a group of cabmen at Haverstock Hill. By this time, all three parties involved in the chase are in cabs: first the anarchist in a great hurry, then the bacteriologist in hot pursuit, then his wife with his hat and coat pursuing him in turn. Thus, it must have been some time in those "few minutes" offstage that the bacteriologist gets in a cab.
(Quote above taken from the story's full text available online.)