There are several options for getting business insurance for pet sitting. Below are links to their websites.
Business Insurers of the Carolina's have various insurance policies depending on what type of pet care you offer.
If you want a discount on their Insurance you can also join Pet Sitters International, they have a member discount.
Pet Sitters Associates also offers business insurance for pet sitters.
Some people have checked with other insurance companies to get a cheaper policy but make sure it covers the specific things that those above cover. Make a list of what the pet sitting insurance covers and ask if they will cover those instances, remember all insurances are different in what they will cover.