Hey carlbenbow,
To do this you will need to first ensure you have the billable expense feature enabled by going to the Cog Wheel > Expenses > Bills and expenses > Turn 'Make expenses and items billable' on.
Then create an expense for the mileage, and tick the 'Billable' box on the category detail line. Save the expense and then create an invoice to the customer, the billable expense will show on the right panel under 'Add to invoice' - select add and this will populate the invoice with the expense details.
Thanks