Do you think it's right for a bank to charge me $35.00 because I am stopping an automatic payment from my checking?
You could choose to keep it going and the new company will withdraw the money, then you'll have to ask for it back. Will your bank let you do this for free 30 days out or something like that?
You stop the ACH withdrawal at the insurance company. If you want to do a stop payment with the bank to keep them from taking it, they'll likely charge you a fee.
Any stop payment at any bank is charged for.