She's adorable! What a tiny little baby!
As I understand common domesticated mice are all descended from the common house mouse. They don't have specific breeds like dogs. There are several varieties however, like satin, long hair, brindle, or even dwarf.
But her variety, from the pictures, looks like a standard black self mouse. She doesn't look small enough to be a dwarf, but she is quite little. She still looks like a juvenile, though I'm thinking she'd have to be at least 8-12 weeks old and pretty much full grown.
Since female mice really do thrive in colonies rather than alone, you might want to consider getting her a/some new friends. If your other mice were picking on her, you might want to look at the idea of getting a younger mouse, who will both be more open to new friends, and being younger, will not be as territorial. You also might want to take the time to pick a mouse who has similar color/look/temperament to her. (You can learn a lot by asking to handle the mice or being allowed to put your hand in the cage.)
I say color/type/temperament as kind of an educated long shot. See, the pet stores around me tended to get their mice from the same mill breeder. I had many, but noticed before long a difference in behavior in the varieties. For example, I noticed that the dalmatian mice from this mill breeder tended towards very skittish, aggressive, and OCD. That indicated to me a strong genetic component. And although this is observational anecdotal evidence (backed up very loosely by similar observational evidence from a couple of rat breeders I know), there seemed to be a minor 'preference' of mice who were similar to gravitate to one another. Perhaps they recognized a similar genetic scent signature, perhaps they were mildly imprinted on a look from birth. Perhaps they were just genetically similar in temperament. I don't know. But it seemed to very loosely result in slightly easier bonding. It also might explain why your albinos didn't take to your black. I don't know.
Anyway, good luck with her! I have a special place in my heart for little black mice.