Oh my .. you definetely don't want to just use a phone call. Are you going to be working as an independent biller, employee, your own business? There are NUMEROUS things you need to do before you just "start billing". You'll want proper agreements in place BAA, contract, etc. You will need either billing software or your own HIPAA compliant login to their billing system.
There are a lot of steps in between for you to do this. Be very careful of your own liability here.