I may have just overlooked it in the rules, but do bombs effect both parts of a huge ship (assuming both parts are in the area of effect), or just one? Who decides which part is effected?

Just one section is damaged, chosen by the opponent.

From p.3 of the Huge Ship rules, under "Damage":

If an effect would damage both sections of a huge ship, the opposing player chooses one section, and the chosen section suffers the damage.

And in case you're asking about non-damage effects, like Ion Bombs, those don't care about which section they hit, since the tokens are assigned to the ship as a whole. If an Ion Bomb is dropped in range of both sections of a huge ship, its effect would only be applied once.

That is what I figured, but it's good to have the page reference