I would like to change my AppleCare payment to another credit card

Check this out.....https://support.apple.com/sl-si/HT201266

This is the right answer. Best Buy can change what card your AppleCare is charged to, if you bought it through them. Call their customer service number at 1-888-BESTBUY. My AppleCare was not being charged through iTunes and changing my payment information there did not solve the problem.

You need to call Best Buy as they can bested advice you.