A bit means a little. It is quite common in informal British English.
- Can you move a bit? (= Can you move a little?)
- Can you speak a bit louder? I can’t hear you.
- Will you wait a bit?
- We were a bit late.
- I was a bit worried.
- I don’t want to go out now. I am a bit tired.
- The watch was a bit expensive; nonetheless I decided to buy it.
- She is a bit old to wear those short skirts, isn’t she?
We do not usually use a bit and a little with adjectives expressing positive ideas.
- The film was a bit boring. (BUT NOT The film was a bit interesting.)
A bit of a
A bit of a means rather a. This expression is used before some nouns.
- He is a bit of a fool.
- I have got a bit of a problem.
Not a bit means not at all.
- I am not a bit worried. (= I am not at all worried.)