If you just have one, yes you can probably keep this bird with Coturnix.
What sex is the Bobwhite? (white and black mask on the face is a male, buff colored face is a female).
It probably doesn't matter what sex it is. Actually females can be more aggressive than males. But being just one Bob, this single bird is unlike to bother the other Coturnix.
Of course watch them all carefully to make sure. Introduce the new bird slowly from a sectioned off part of the pen or cage. Don't just mix in a new bird to an existing flock. Can cause chaos and blood shed. Keep the new bird separated by wire for a couple weeks. Everybody sees, nobody touches. After a couple weeks you should be able to mix them together without too much arguing.