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.