by the bye vs apropos

by the bye is not an adjective while apropos is an adjective.

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

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

Other synonyms of by the bye include by the way, incidentally.

by the bye (adjective)	apropos (adjective)
	of an appropriate or pertinent nature

by the bye (adverb)	apropos (adverb)
introducing a different topic	at an opportune time
	introducing a different topic