Travel time is billable. Unless flying, driving from home to the airport or from the airport to home is non-billable. Flight time is billable. All driving at the location is billable.
As soon as you hit the hotel, you are off the clock.
Considering it is a long time client, you could offer a lower hourly rate for travel. Personally I am against that practice. If I wasn’t traveling for that client, I could be doing a job for a different client at the full rate.