"A little bit" and "a bit"

A little bit and a bit are common idiomatic phrases in English meaning "a small amount."

Editor Neil Serven helps explain this idiom:

This phrase may sound redundant because the word bit on its own can mean "piece" (as in "a bit of news"), so "a little bit" is often preferred to reinforce the idea of smallness.

While it is more common as a noun phrase (as in "a little bit of food"), it can be used adverbially, as in "I was a little bit sore after running" [=I was somewhat sore after running].

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The phrase a bit on its own can be used for both applications.

As a noun: 

I had just a bit of cake at the party.

As an adverb:

The movie was a bit dull.