Hi there, hirscheric,
The option to bill a customer without sending an invoice is currently unavailable in QuickBooks Self-Employed (QBSE).
In QuickBooks Online (QBO), you can set up a recurring sales receipt to collect payments every month.
To avail of this feature, you need to sign up for QBO. Use this link to see the comparison of the product: https://quickbooks.intuit.com/online-compare/. Then, click the Free 30-day trial to explore the system.
I've added the Switch from QuickBooks Self-Employed to QuickBooks Online article to learn what to do with your data before moving.
Keep me posted if you have follow-up questions. I'm always around whenever you need help.