"a bit" is a small piece, quantity or amount of something.
So, a "little bit" means "a small amount or quantity".
e.g. I like that movie, but only a little bit.
So, a little bit means "a little (small) bit (small amount), and this looks like "a little/small amount of a small amount". It looks like it's "a little small amount", but "little" is an adjective that is describing "a small amount of something (bit)".
Bit is usually used to say "amount".
"A little" means the same thing. The word "bit" is not included, but it is understood, e.g. I liked the movie a little = I liked the movie a little bit.
The three exressions are not exactly the same, but they are very similar (equivalent).
Hope my answer helps a bit/a little/ a little bit :)