Synonyms for By the bye:

adv

•by chance (adverb)
incidentally.

adv.

•all (adverb)
by the way, incidentally.
•by the way (adverb)
incidentally.
•incidentally (adverb)
by the way.

n.

•by the bye (noun)
by the way, incidentally.

Other synonyms:

•adv
by the way.