Green’s Dictionary of Slang

1. (US) of a person, to move (fast).

1905		Wash. Post 15 Jan. 4/3: The young man of tender years [...] has a vocabulary which would put Webster to shame [...] When the young man moves, he either ‘skates,’ ‘oils his castors,’ or ‘trolleys.’.
1914		Ade ‘The New Fable of the Speedy Sprite’ in Ade’s Fables 23: Loretta trolleyed herself down into the Noise Belt.
2001		‘John le Carré’ Constant Gardener 501: When did you ever put on your best suit, trolley round to the Blue Boys headquarters, and accuse them of mounting an orchestrated cover-up and taking Kenny K’s shilling for their trouble?

2. (US) to travel by tram or trolleybus.

1915

G. Bronson-Howard God’s Man 281: I was standing shivering on a street corner last winter, me and Beau, not a bean to get the ham-an’-eggs outa hock, not even to grab a short and trolley ourselves down to Mother’s. [Ibid.] 382: If you miss the nine train [...] You’d have to trolley to Northport.