I used to bill one-half the hourly rate when I travelled to the client's site. If the drive time was 30 minutes, I'd charge a minimum of 2 hours plus 30 minutes for the drive. That would add up to $125.00.
Over the last five years or so, I changed that to a higher rate for the first hour. Now I charge $90 for the first hour, and $60 for subsequent time. A typical half-day outing will be $210, minimum.
In most cases you'll find that it does not help to reveal your hourly rate. Try to bill for the total work you accomplish. However, the company might set the rate, and then you have no choice. Always take money that is offered, unless there is a better task out there for you.
BTW, set a limit to how much credit you'll extend. There are many companies that will string you out for months, and continue to bring you in to do more work, always promising more work, never paying. Remember, you're not in the lending business. Your bills must be payed in less than thirty days, and you should get the same condition from the company.