Consider charging clients after you complete the service they requested. If there are third-party charges involved, suggest they pay those directly or bill those up-front at cost for their convenience.
When doing public relations work, for example, you might begin the project by writing a news release and getting the customer's approval. Next, you might offer to show them how to create an account on a distributing service such or show them the price and do it for them instead. Finally, you would submit the release and then submit a bill along with a report of the results.
The alternatives you choose should adapt to your customers rather than vice versa.