Upload & Sell: On
If you made the drive on Tuesday & Thursday (long day I know) ... how would you charge?
Also, if you were hiring a camera repairman to come to you to work on your gear at your location, how would you expect him to charge you for his travel time?
Time is time ... the value of it is one thing. The cost of mileage expenses (plane, train or automobile) are different things (gas, oil, tires, depreciation @ standard IRS rate, etc.).
Whenever I travel for other (non-photography) industry work, I'm "on the clock" while traveling, even if they pay for 100% for the plane ticket up front, etc. When I'm working for someone else (as in a regular employer or contract staffing firm), they might be the ones paying for my "on the clock" time, which is being absorbed into their overhead that they are passing through to their client, or they just count it as "billable time" that they present separately to the client. It can go either way, but it still is getting paid.
If my agreed upon hourly rate is "premium" I may choose to absorb my time into it. If my agreed upon hourly rate is "low margin" ... I may not have any room to absorb the cost of my time.
But, when working for yourself, you are now the one responsible for billing sufficiently for your "on the clock" while traveling. Whether it is billed separately as "travel time" & "mileage" or as "expenses" or built in to your billing otherwise (part of overhead) is largely a matter of semantics & presentation (and tax accounting).
The salient point here is that SOMEBODY (me, employer, contract house, client) is paying for those costs of "time" and "mileage". It's your call at who is responsible to cover those costs. Imagine if the client asked you to go to the South Pole ... how would you charge for the travel expenses of time & money? The issue becomes a bit more clear when exaggerated as such, in that you would either have to raise your "rate" to be able to "eat" the costs ... or you'd have to bill for the travel time/expense separately ... or you'd have to "pass" on the job because it would no longer be sufficiently profitable due to the erosion of you margin by your travel costs (time & mileage expenses).
Most business realizes that travel has an external cost. They also understand (sometimes needing a reminder) that it needs to be a profitable endeavor for you as well. They don't want their margins eroded by others imposing on them costs that they wouldn't normally incur, it is only reasonable that you be extended the same. Whether you are on "premium" or "low margin" rates will have some input regarding your approach @ 1/2 your normal rate, full rate or none. Do the math for the gig "cradle to grave" and see how you fare overall regarding your margin. That will give you some insight as to whether you are "eroding" yours vs. "gouging" theirs.
If it only takes you a 1/2 day of travel, then bill for a 1 /2 day of travel. It will be your decision as to whether to leave the day before or very early the day of. They typically only want it to be fair. Ask yourself, how would you expect them to bill you if it were reversed ... and proceed accordingly.
Here's a reverse thought. If you could "Beam me up, Scotty" to their location ... how much would you charge for your time to get there? Likely none for the time ... but the cost you paid Scotty to get you there (in minimal time) would be one that you would pass on. Slow boat to China or Concorde across the pond ... time & money.