incidentally vs by the bye

incidentally and by the bye both are adverbs.

Word	Noun	Adjective	Verb	Adverb
incidentally	No	No	No	Yes
by the bye	No	No	No	Yes

As adverbs, incidentally and by the bye are synonyms defined as:

Other synonyms of incidentally include apropos, by the way.

incidentally (adverb)	by the bye (adverb)
introducing a different topic	introducing a different topic
of a minor or subordinate nature