You are using billable time incorrectly. It should only be used for recording time. This is because entries are posted automatically to Billable time and Billable time - movement. The latter entry is transferred to Billable time - invoiced when the invoice is created. You would not want to have various travel costs mixed into such accounts.
Further, custom fields for billable time apply only to the transaction form. They cannot be made to apply to line items.
The proper way to account for such travel costs is with billable expenses. Read these Guides: