what is owners liability coverage in case of dog bite?

In all states of which I am aware, owners are responsible for the pet's behavior in all situations, except those arising out of negligence/abuse or a crime (like a robbery). If you give someone permission to be on your property, you are responsible for any damages that person sustains during the interaction with your dog. In most places, anyone witnessing a dog bite is required to report it to Animal Control.

I woud look at your homeowner's or renter's insurance policy to see if warranties are available for dog bites. Many policies have specific coverage (or exclusions) for those matters.

No, there is nothing for the sitter. Rover doesn't provide insurance, only some guarantees for the pet owner. It is all described here:

https://www.rover.com/guarantee/us/