"I think I have the GL Billable Expense account"
There is not typically a single account like this. "Billable" is a Status or Function. The Expense still is the expense as usual, for purposes of tax form reporting. Billable or not has to do with:
First, assing that it relates directly to a customer
Second, showing you intend to Charge it back to them, or "sell" it
That means Billable Costs include expenses such as Supplies, subcontractor labor, materials, travel such as Lodgin and airfare. Those are Tracked as expense the same as always, whether "to be reimbursed" or not, whether to be Charged at cost or a higher price, etc.
Expenses show on the P&L becuase you incurred them.
When you charge that to the customer, you want to see this result in Data flowing to Income. Make sure you did not end up with Expense reduced by Negative Expense, because of how you set up the charges to the customer. That would explain why they "disapeared" from the P&L. Look at your Detail reports, to see the individual entries that are posting to your accounts. Negative Expense should really be an Income activity.
