Many companies do not care so much that a dog bit someone (ok, yes they do care) but it is the fact that there was a claim. I work for State Farm Insurance, and we will write insurance for people if they have had a dog bite claim. But…that would need to be a claim that has happened at least 36 months ago before we even consider it, amongst several other factors. Keep in mind that it may not be the company as a whole that is turning you down…it could be that select office/agent that you are contacting. State Farm Insurance as a whole does not have any breed discrimination policies. But, there are individual agents out there who may have a bias againist certain breeds and decide on their own NOT to write policies for anyone who has a certain breed.
Many companies will also allow you to keep your dog and your insurance, yet exclude him from coverage. Basically, if there were to be another incident, the company would not cover the incident. Though that could be dangerous with a dog who now has a bite history, but it would be a temporary solution in the meantime until you locate a company who can write insurance for you. There are companies out there. They can just be hard to locate.