This is not explicitly spelled out anywhere to my knowledge. However, the alchemist gains a singular bomb ability, and then alchemist discoveries can be used to “modify” bombs:
Discoveries that modify bombs that are marked with an asterisk (*) do not stack. Only one such discovery can be applied to an individual bomb.
That suggests that even when you apply different discoveries to your bomb attacks, you are still using the same bomb attack, just modified by one discovery or another.
The phrasing of individual bomb-modifying discoveries, such as anarchic bombs, also back this up:
When the alchemist creates a bomb, he can choose to have it deal chaotic divine damage. Lawful creatures that take a direct hit from an anarchic bomb must succeed at a Fortitude save or be staggered on their next turn. Against neutral creatures, anarchic bombs deal half damage, and such targets are not affected by their staggering effect. Anarchic bombs have no effect on chaotic-aligned creatures.
“When the alchemist creates a bomb” suggests that the “anarchic bomb” is still “a bomb” and should be affected by Ability Focus (bombs).
This seems different, to me, from hexes, which are each a separate effect, simply all chosen from the same list. The alchemist’s analogue there would be the discoveries themselves—the ruling on Ability Focus (hexes) probably should apply equally to the idea of Ability Focus (discoveries).
Ultimately, though, you’ll have to ask your GM. For that matter, Ability Focus is a monster feat: Paizo’s recommendation is that players clear all monster feats with the GM before selecting them, so you probably have to talk to your GM about it anyway. Personally, my games ignore the rulings about monster feats and about Ability Focus and hexes (and that carries over to discoveries), but that’s my game.