Dub, interesting, our friends have a Bichon, and from the day they got him, he pees on certain things,certain rooms,etc., while the "shelter dog" they have is great.
I'm not an expert, but the toys and terriers tend to have a "peeing problem", personally I have never had that problem with my dogs, and my parents never had that with their dogs, and together we have had many dogs, mutts, as well as pedigrees.
But like anything else, a person has to really be into the breed and fully know as much as possible about the breed, before making a decision. If the dog is just for emotional support and not a service dog, I'd say breed or mixed it doesn't matter. As far as a Service dog, I really do not see a Bichon as a Service dog.
You have to do what your heart tells you, when deciding on a pet, what your needs as well as the dog.
I wish you loads of love,luck and good health.
And of all things, happiness with what your choice is, and happiness for what choice of pet you have.

DE