Humble Bundle Not Listed

Which Humble Bundle? If you wait a day or so it'll probably show up on the list.

"Should I just select one of the games from the bundle and giveaway the whole bundle through that one giveaway? Is that allowed?"

Yes, that is perfectly acceptable.

I'd recommend making a support ticket - maybe the mods will manually add an option for the bundle.

Depending on the bundle you can also split it up.