do a bit
1. To do only a small amount of something. I was only able to do a bit of cleaning before your mother called—that's why the dirty dishes are still on the table. A: "Did you write your essay?" B: "I did a bit, but I decided to take a break.
2. To tell a joke or perform a short comic routine, especially when done in a satirically serious or sincere manner. The comic has such a dry sense of humor that it can sometimes be hard to tell when he's doing a bit or actually being serious.
do (one's) bit
To make an individual contribution toward an overall effort.