Welcome to the Community, @bebasin.

I am here to give information about your inquiry regarding the billable expense being charged to your customer in your QuickBooks Online (QBO) account.

In creating a bill in QBO, it does not automatically assign to a project or charge your customer when you mark check the billable box. 

If you want to assign to the project but not charge the customer, you can select the Customer/Project but don’t tick the Billable box.

You can read more about creating a billable expense by checking this article out: Enter billable expenses.

Let me know if you have further concerns about creating a bill in your QBO account. I’ll be here to assist you at any time. Have a good one!