Hi Sara:
Rover's insurance is a secondary insurance policy, and has basic coverage for the pet owner with a $500 deductible. It does not cover sitter's liability. Every sitter should have their own pet insurance to cover liability at minimum. I'm sure many sitters don't. There is no workers compensation coverage either because as a Rover sitter you are an independent contractor, not an employee.
There is a lot of ignorance regarding bonding. Bonding is only needed if you have your own business with employees - to protect against employee theft. You as a solo business owner (or independent contractor) would not steal from yourself, so you would not need bonding. If one of your client's accused you of theft, your liability insurance would cover that.
Still, some sitters pay extra for bonding coverage because so many people - clients and sitters alike - don't understand what bonding coverage really is. So it's up to you which type of insurance to get, but you should at least have your own basic liability coverage.