n. a jail sentence. (Underworld.) : Mooshoo did a two-year bit in Sing Sing.
n. a small theatrical part. (From bit part.) : It was just a bit, but I needed the money.
n. any part of an act; any isolated activity or presentation. : I didn't like that bit concerning penalties.
Dictionary of American Slang and Colloquial Expressions by Richard A. Spears.Fourth Edition. Copyright 2007. Published by McGraw Hill.
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American Heritage
Idioms & Phrases
do one's bit
Also, do one's part. Make an individual contribution to an overall effort. For example, You can always rely on Anne to do her bit, or I'm anxious to do my part as a board member. [Early 1900s]