bit by bit vs step by step

bit by bit and step by step both are adverbs.

Word	Noun	Adjective	Verb	Adverb
bit by bit	No	No	No	Yes
step by step	No	No	No	Yes

As adverbs, bit by bit and step by step are synonyms defined as:

Other synonyms of bit by bit include gradually.

bit by bit (adverb)	step by step (adverb)
in a gradual manner	in a gradual manner
a little bit at a time	proceeding in steps