I know, it's not really a spell casting class, but functionally they work the same.
So, could a half elf pick Bifurcated Magic, go Alchemist 1/Wizard 1, and cast those spells or brew those potions at caster level 2?
Good news is that Bifurcated Magic does not actually specify it has to be a spellcasting class; you just select 'two classes'.
Furthermore, as the alchemist uses their level as the caster level, actually not having a caster level doesn't seem to be an impairment; it would seem you can give it the +1 bonus regardless.
Awesome, thanks.