Possible meaning of bicycle

I know that a bicycle is a vehicle that has two wheels and is moved by foot pedals, but I am sure this is not its meaning of the word in this conversation taken from a U.S crime movie released in 1947:

CONVERSATION:
Daisy: What do you think it is? A lover's quarrel?
Larry: Well, if it is, that boy must have a bycicle, but Paris wouldn't.
[when Larry says "that boy" he refers to Jeffrey]

CONTEXT:
Daisy and Larry are talking of a couple that is arguing in the same bar. They are Margaret (married to Steven) and Jeffrey (married to Paris). Larry is always joking, Daisy is his girlfriend. Steven and Paris are not in the bar.

Obviously, neither Margaret nor Jeffrey have bikes. Jeffrey is a businessman. Margaret is a housewife. We don't know what's the relashionship between them, only that they meet secretly at this bar every now and then. Larry knows who they are.

If "bicycle" is some slang word for "lover", "secret" or "drunken spree", it might make sense, but I haven't found anything to back up this idea. Urbandictionary.com says that bicycle can mean "slut", but I doubt that this was a common meaning for the word in the 1940's.

Any clue about what a bicycle could be in this context?
Could it mean "drunken spree", "bender", "blotto", "lover", "prostitute" "secret" or something else?
Remember that the action takes place in 1947.