Hi @ken63,
I'm here to share insight on your query about Online Bill Pay in QuickBooks Online (QBO).
Since a bill payment transaction is an expense, the accounts that show up on the drop-down menu will be Expense accounts. Other types of accounts won't be available due to this reason.
If you're looking to record billable expenses instead, see this article: Enter billable expenses. This includes a short video that acts as a reference for this process.
Do you have other questions in mind? Place them in the comments below, and I'll get back to you.