Eye Stain is caused by the eyes running and the dampness of the coat around the eyes allows bacteria to grow and cause eye staining. Many breeds of dogs have eye stain, but because the Bichon has a white coat, it is more noticeable than in other breeds. Not all Bichons have eyes that run. Some do not run at all, while others can run often.
What can be done about it? I would love a Dollar for for every time I have been asked this question. There is no easy answer. Regular wiping of the eyes, say, two or three times a day, will help keep it in check - but will not prevent it. You can use eye lotions etc., and some of these will work quite well. There is an Eye Stain Remover sold by the Southern Bichon Frise Fanciers Association in U.K. which works quite well (click here for info on how to buy it), but at the end of the day, eye stain is something you may have to live with if it affect your dog.
Hot spots are somewhat rare in Bichons from my experience, but they may occur in some dogs. Often they are caused by a food allergy, and sometimes can be hormone related - eg when the bitch is in season etc.
If hot spots are a problem, then I would suggest that you consider a change of diet. In my opinion the best food available on the market today is XP3020 Xtra Premium Dog Food. It can be difficult to find, but I can tell you it is worth the search. It is the best food on the market and only costs $55.00 for a 15kg bag. You can find more information about this fantastic food on www.xp3020.com.au.
If your dog is affected badly by hot spots, you may need to seek Veterinary treatment in the initial stages to provide some relief for the dog. Some Vets may advise a change of diet onto a Chicken and Rice diet, in which case XP3020 would be fine as it is chicken based.
Scratching can be a problem for some dogs. Like Hot spots, scratching can be related to a food allergy, but may also be caused by an allergy to something in the environment, or caused by flea bites.
Lets deal with the easy one first - flea bites. With the new treatments available today eg Frontline and Advantage etc., there is no excuse for your dog having fleas. These products break to life cycle of the flea, and will actually rid the surrounding environment of fleas altogether. They are not cheap, but they are definitely worth the money you pay for them.
If the scratching is food related then as for Hot spots change your diet. If it is an allergic reaction to something in the environment, the problem can be more difficult to solve.
I would always suggest diet change as the best starting point for any scratching problem. The reason I suggest this is that an allergic reaction may in fact be multi-factorial ie caused by the dog being allergic to more than one thing. Each allergy increases to allergic load to a point where the dog goes above its scratching threshold and starts scratching. For example, the dog may be allergic to say beef, wheat, dust mites, and pollen, and the total combined allergic load will cause the dog to scratch. Every day the dog is fed food containing beef and wheat, and is exposed to dust mites. But this total allergic load is below the scratching threshold, so the dog does not scratch. But come spring when the pollen is in the air, this pushes the dog above his scratching threshold, and bingo, one scratching dog. So change diet and while the dog is still allergic to the pollen and dust mites, he might just stop scratching.
If this doesn't work then it is a matter of eliminating as many of the allergens as possible to bring the dog under its scratching threshold.