Bichon Frises tend to be happy little dogs that get along with everyone and all other animals. The big drawback to them is the grooming bills unless you learn how to cut their hair yourself. They have hair that doesn't stop growing so they need regular haircuts. The main thing with small dogs is to remember they are still dogs. Anything that you wouldn't allow a big dog to do shouldn't be tolerated in a small dog. That is how a lot of small dogs become overbearing and nippy.
I would love to have dogs that liked my cats. I now have (until 3 wks ago I have 4) 2 doxis. They want nothing more to do that eat the cats. Well, they were here before the kittens. THen I found a couple of kittens in my barn with my barn cats, (all are spayed and nuetered.). I kept one, spayed her, tipped her ear to send her back out. No way. I feel in love with her and she stays in the house. Then I got another feral kitten from a TNR group and they stay in the back of the house. there is a kiddy gate in the hall, so the cats can get back and forth but the dogs cant. I have gotten so tired of the dogs chasing the cats, that I brought Smoke to the bedroom, put her on my chest, and let one of the dogs come up to her. In this situation, I knew the cat would teach the dog some respect. It worked. as long as the cats don't run. When they run all bets are off. It's only been a couple of months so I know I still have time before I get too frustrated. Oh well, it is a long process, but I know it will get better.
I have a friend with a toy Maltese, and he is great with her cats. He is also sooooooo adorable. I would take him in an instant if she would only part with him. She even got him at a shelter with a 3 puppy litter was brought in. They were about 8 mo. old, and a mess.