Yes, there are a couple of ways another individual can book a trip for someone.
The 3rd party would ring the dispatcher and book the trip. This is booked the normal way and the 3rd party would give the passenger's information to the dispatcher.
It is possible to add people in the dispatcher who are authorised to book trips for specific accounts. The 3rd party would provide the dispatcher with their name and pin and if this is correct then they can go ahead and book from the account and have that account get charged.
To add users to an account from The Dispatcher, go to Manage -> Invoices.