Schnauzers are good. Your friend would prolly want a mini schnauzer.

They are great dogs that get along with dogs and cats. They are non-shedders, no doggy odor, extremely smart. I'm pretty sure they can go into a bag, but not sure about that one. They are also really friendly, and are good house watchers.

Maybe a poodle would be better if she wanted it to be in a bag, but schnauzers are great!