Would it be against the rules to put a request in the Subeta Pets form asking someone to help transform my pet into a Bhakoru/Bumbus?

Nope, that's fine c: Just a note that you can only transfer a pet every 30 days, so you'd have to go through the pound to send the pet to the other person, if you wanted it immediately (I don't believe Bhakorus or Bumbii are able to go through the pound, I think they get transformed into a Kumos if you try~)

I can confirm those two species when placed into the pound will become kumos. HTF if you're account is old enough I'd do what Darkrai suggests and have the person helping pick the pet from pound (or make a new one if you feel transferring that specific pet is risky) and then when it's been transformed have them friend you and send it back. If your account isn't old enough to pound a pet and you want the pet asap the only option will be a new created pet.