Well, ifif the key is Bb major, then Cb should be bII in that key, pretty much no matter what its purpose is. Unless there's some modulation or weird temporary tonicization going on, Cb is correct - there should be only one "B" note in a key, and Bb already fills that spot. GuitarSome guitar players may gripe about it, but it's better form to write it correctly as Cb. If the key were E major, you'd obviously write it as F, not E#, so here in Bb, write it as Cb.
Of course, nothing's stopping you from leaving some editorial note that Cb = B somewhere obvious in the lead sheet. If you do that, you can likely preempt any whining!
No matter which option you pick, Cb or B, you're going to get some dissatisfied customers. I personally would choose to write correctly and give beginners the chance to grow their theory knowledge rather than make things more obvious but annoy the more advanced musicians, but you might have reason to decide one way or another depending on specific circumstances.
Also, I would strongly advise against a rewrite in A# for the same reasons you identified yourself. A# major is a nasty key (with 10 sharps in it); don't use that unless you have to.