By default, an alchemist's bombs are not affected by spell resistance, because they are a Supernatural (Su) ability.
Only spells and spell-like abilities are subject to spell resistance. Extraordinary and supernatural abilities (including enhancement bonuses on magic weapons) are not.
However, there are a few bomb discoveries that duplicate the effects of spells which can be affected by spell resistance; namely plague bomb:
Benefit: The effects of the smoke created by an alchemist’s bomb duplicates the effects of contagion instead of fog cloud, filling an area equal to twice the bomb’s splash area for 1 round per level.
and cursed bomb:
Benefit: When an alchemist creates a bomb, he can choose to have it deliver a debilitating curse. A creature that takes a direct hit from a cursed bomb must succeed at a Will save or be affected by bestow curse.
In either of these cases, would spell resistance apply? Note that neither of these discoveries on their own have the (Su) tag.
Best Answer
No, spell resistance doesn't apply
Regardless of the type of the bomb, either extraordinary or supernatural, neither allows spell resistance, that is unique to spells and spell-like abilities. Though I agree that the ability type should have been made clear on all examples, they default to supernatural abilities when no type is given, as that is the type of the Bomb ability from the alchemist class.
According to the SRD, only two discoveries are spell-like abilities: