I appreciate the response - thank you for your time; unfortunately, I don't think the response addresses the question.

I am aware of how to tend to a regular expense/check against an account in QuickBooks. 

The problem is this is a bill through a vendor account not connected with a credit card or bank account.  I create a bill for these purchases, they aren't checks or regular expenses, so the process you referred to, which is familiar to me, is not applicable in this situation.

Also, I'm not making a bank deposit to reimburse the company, I'm taking it out of my client's paycheck.  So, the reimbursement method described does not apply in this situation either.