A Homeowners policy is based on the current condition of the home and the owner of the home. If the new owner has a history of claims, that can follow you to your next home. The fact that a bank owned the home will not effect your new insurance policy when you buy the home but the current condition of the home may effect which company will insure the property, the coverages they will offer, and how much they will charge. Homes with repair issues like an old roof, missing or damaged siding, and water damage inside the home are some issues you can encounter with a ban kowned property. They are properties that are sold as is. The damage could be from the previous owner who obviously was not financially able to maintain the home or the bank may not maintain the home since they are in the business of home lending and not property management.
Depending on the condition of the home you may have to get insured with a speciality homeowners insurance company until you can repair the home at which point you can pursue a more traditional policy which will usually have a lower rate with better coverages.