Question about travel expenses

[Anonymous]

I have been a tenporary employee for a large company for almost 3 years. I get paid through a staffing agency. The client where I am assigned asked me to work at an event that is a 4 hour drive from our office. They said they would provide a hotel room for the night before (Sunday) because the event starts at 8:00am Monday. I know they will pay for my gas mileage. I should also bill for my travel time and meals the night before correct?
Another question-Everyone has purchase cards. I do not since I am not a permanent employee. Is it appropriate for me to ask my supervsor to book the hotel room on her card (she is not attending the event but other people from the department are) so I don't have to pay out of pocket and be reimbursed? Or is that a conflict since it is not her trip?

[Anonymous]

I've booked travel for my non-perm direct reports on my corporate card, but I'd ask your staffing agency what the protocol is. They probably have this detailed in a contract somewhere.