Most of the public relations professionals I've spoken to agree that you have to bill for time if a specific client requires the trip and prevents the consultant from serving other people. The time charged must be the actual time minus 1 hour for the journey that is considered reasonable. When calculating distances, it's always from office to client, from client to client, or from office to office. Most consultants who travel more than me bill for travel time.
Some bill at their full hourly rate and others bill at half their hourly rate. There's usually a limit of 8 to 10 hours a day, even if the trip lasts longer. Most people try to do as much legitimate, billable work as possible while traveling and bill for that time at the full rate. At the end of the day, it's up to you to decide what's best for you and your customers when it comes to travel time.
Time is tracked throughout the project (including travel time) and any excess that exceeds the minimum hours initially estimated is billed. I bill for packing my bags and I exaggerate my actual billing for the days of travel to account for the stupidity that trips are not billable. My company pays for my travel and hotel expenses, but cannot charge them to the customer (they are covered by my daily rate). For us, travel time is considered rest time by law, that is, not working (unless you drive yourself), and not only is it not billable but it is not paid.
I think a reasonable option is to charge more than the normal trip to work. It's the only option that really makes sense and that encourages teams to go to hotels. I have a couple of colleagues who travel for all their work, so they include the trip in their regular fare or rates.