Health
Bichons are generally healthy, but like all breeds, they're prone to certain health conditions. Not all Bichons will get any or all of these diseases, but it's important to be aware of them if you're considering this breed.
If you're buying a puppy, find a good breeder who will show you health clearances for both your puppy's parents. Health clearances prove that a dog has been tested for and cleared of a particular condition. In Bichons, you should expect to see health clearances from the Orthopedic Foundation for Animals (OFA) for hip dysplasia (with a score of fair or better), elbow dysplasia, hypothyroidism, and von Willebrand's disease; from Auburn University for thrombopathia; and from the Canine Eye Registry Foundation (CERF) certifying that eyes are normal.
Sources: Wikipedia, Dogtime, Bichon Frise Personality, CKC