Yes a small heater is advisable.
Also, female Bettas are definately NOT going to even look at your Bristlenose, lol. They would love to eat baby shrimp, but seriously those girls won't bother anyone. Even a male wouldn't bother pestering any type of catfish. That's been my experience anyway. The only fish that Betta's usually enjoy harassing really are live bearers like Platies because they are of a similar size and very bright colors so Betta's will usually flare up at them and scare them away, but I have never seen any Betta nip fins of another species, only other Bettas if they get the chance.
That's good to know. Even though I said I'm just gonna leave the betta out, deep down inside, I still really want it lol Maybe I can keep shrimp in another tank. Would female bettas bother CPDs? I'm not sure whether or not they're considered "bright." They definitely aren't on par with the betta size-wise.