Hey there, MJT.

I'm by no means an accounting professional, but I do have some insight to provide regarding your setup.

Just to clarify, when you say Admin account, are you referring to the Accounts Payable account? If so, then I can see that your setup is correct. To verify this, you can check the Transaction Journal for both your bill and it's payment. I'm attaching these screenshots to show you how it would look like.

Bill Transaction Journal

Bill Payment Transaction Journal

Let me know if this isn't quite what you're looking for, I want to make sure this is taken care of. Have a great day!