"A bit" is similar to "a little", "kind of" or "somewhat". It's used when you want to lessen the degree of a description:

He's a bit shorter than me.

He has a video of me from when we were in college that's a bit embarrassing.

"A bit" is used for adjectives that are negative. So you wouldn't say that an event was "a bit fun" or that a person is "a bit nice". But you can say that the event was "a bit boring" and the person is "a bit rude".

"A bit" is slightly formal. It's more formal than "kind of" or "a little", but more casual than "somewhat":

kind of > a little > a bit > somewhat