Well you can go about it a couple of ways. Fuel reimbursement plus vehicle operating cost per mile plus what ever you think you should charge for your windshield time. Then there's always the IRS mileage guide plus windshield time. I've used both before, some folks like the first one others like the second, it just depends on who you're working with and how you present it to them..
Short job, I'd generally go with fuel plus hours for the driver. Others can sleep, read, whatever but not on the clock. That, or they can drive themselves there as most construction guys do. At their own expense.
At a minimum, $800. Based upon .50 per mile. Plenty for fuel and vehicle use with a little for food. I believe the current max for taxes is .60. That doesn't mean you can't charge and/or pay more, it is only what is tax deductible. Your $1 per mile would be vehicle and wages for the driver and be a bit generous at that. And as you said, taking advantage of the customer (my words).
A longer job you could pass on the travel because the bid would cover it. But then you really want to figure some kind of per dium. Lodging, food, fuel.
Have a Great Day, Brent