I'm at a loss as to what the problem is. You wrote that you recorded a deposit in your bank account in QuickBooks, listing the vendor name and amount and the AP account. If so, then you're done, as far as keeping records in QuickBooks to match your bank account.

Then you wrote how you applied the credit the deposit created to a bill.  Then you're done as far as your AP account.  You can ignore the 0.00 check some versions of QuickBooks create when you do this. I don't know why they do that.

Then deposit the check you're holding in your bank, which mirrors the deposit you created to start the process.