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.