I can not comment on a the mix of a yorkie/bichon=Yorkieshon......but I have a 5 yr old pure breed Bichon named Frasier and Cooper and Chloe who are both purebreed Yorkie's. There personality's are day and night difference. Of course each dog is different, but Frasier is what we call a cat/dog....he sleeps all the time, very lazy, laid back gets excited maybe twice a month when the UPS guy rings the door bell....lol. He has been this way even as a puppy. He really NEVER barks, was super easy to house train and the most loving creature I have every known in my life. He does NOT have a mean bone in his body. My 11 yr old daughter has dressed him up in every outfit you can think of including wigs and sunglasses, he has been put in a baby swing, pushed in a stroller, etc and NOTHING ever bothers him. The bad side of this breed is the allergies!!! We have been through so much to help the poor guy. And he has a lot of anxiety issues.
Cooper is total opposite, runs around like his pants are on fire all day long, wants to play ball all day until your arm hurts, can be a little nippy to younger children, and barks much more often, and is of course very territoral with his toys. When it is time for bed though he becomes a our little baby and then just wants to be held, and turns into a total love bug.
Just thought I would pass along the difference we see daily.