I don't have a bichon, but my boys know one, and I think a bichon and Yorkie would make a good pair. It would all depend on the individual dogs and their personalities. Sometimes 2 Yorkies don't get along.
The only other consideration would be size difference. Sometimes tiny dogs coexist perfectly with larger dogs, other times, you have to supervise closely to make sure the smaller dog doesn't get trampled.
__________________ Kristin, Max and Teddy |