I've always said ˌbɒməˈdɪə. I'd no idea that the second b was pronounced, having never heard it actually said.This reaction is understandable, given that the second b is silent not only in bomb bɒm || bɑːm but also in bombing and bomber. However I suppose we all agree that bombard is bɒmˈbɑːd || bɑːmˈbɑːrd (or possibly bəm-), and bombardier is formed from that rather than directly from bomb.
Historically and etymologically the relationship is like that of climb – clamber, thumb – thimble, crumb – crumble. In modern English most people do not feel the items in these pairs to have an obvious relationship to one another.
Other words spelt with a final silent b include lamb, comb, dumb, plumb, limb, numb, and (generally) jamb and iamb. Again, the b remains silent in inflected forms such as combing, dumbest. This gives us the interesting pair of homographs written number: the one to do with counting, ˈnʌmbə(r), and the comparative of the adjective numb, ˈnʌmə(r).
Interestingly, the handful of words with final mn, in which the n is silent, all have obviously related forms in which there is a pronounced n. Thus we have damn dæm but damnation dæmˈneɪʃn̩, and similarly autumn – autumnal, solemn – solemnity, column – columnist, condemn – condemnation, hymn – hymnal.
Phonologists in the Chomsky-Halle tradition see these stems as ending in a final /b/ or /n/, obligatorily deleted after /m/ unless a vowel follows across no boundary or just an internal boundary. But they would also see a similar relationship in pairs such as sign – signal, (im)pugn – pugn(acious), (con)dign – dignity. Let’s not go there: in my view it’s orthographic, etymological, and pretty obvious to classicists, but is not part of contemporary English phonetics.