As pointed out in comments, Anglophones use bullet proof as well as bomb proof. Also note that regardless of whether the usage is literal or metaphoric, we usually write the more common bulletproof as a single word, but bomb-proof is more likely to be hyphenated.
But OP is primarily asking about metaphoric usages. On that front, there's no doubt at all that bulletproof is far more common...
a bulletproof argument - 280 hits in Google Books
a bullet-proof argument - 85 hits (including 2-word versions without hyphen)
a bombproof argument - 2 hits
a bomb proof argument - 2 hits
Another extremely common metaphoric usage (for arguments, at least), is...
a watertight argument - 1920 hits
Focusing more specifically on OP's context, it's probably worth noting that Google Books claims 41 instances of a bulletproof program, but there are only 2 hits for a bombproof program.
One more point relating to the XXXX-proof construction is that bullet-proof in particular can have a far more general metaphoric meaning than non-native speakers might expect. Consider, for example,...
1: He's bombproof. (relatively uncommon; 87 hits in Google Books)
2: He's bulletproof. (962 hits)
...where (ignoring a few possible literal contexts), #1 would always imply that metaphorical "bombs / missiles" cannot harm him. But #2 is also often used to mean He is reliable, He will not let you / us / someone else down (i.e. - asserting that others can rest easy, rather than the subject himself).