For a new mystery shopper, I think it is quite useful to use cents per mile as a basis for giving quick offers to schedulers while under pressure. One simple calculation and you don't have to worry about a complicated formula. Later, with experience, you will want to use many other factors, but cents per mile is a good place to start. (If you shop in a metro area with bad traffic, cents per mile will not work for obvious reasons.)
For me, anywhere from 66 cents to $1 per mile is reasonable, depending on the difficulty of the shop and how badly I want the work. For the calculation, I considered the entire fee (base rate + bonus.) So, for a relatively easy shop 45 miles away, I would have asked for a total fee of at least $60 (90 miles x $0.66). That rate covers vehicle costs; other overhead such as printing; self-employments taxes; and time spent preparing, driving, doing the shop, and reporting. I also try like crazy to add at least one more shop to the trip.
For most shops, schedulers won't go for the $60. But some will, and you will never find out until you ask and stick to your guns. For those that refuse, you at least get a feel for your local market prices. Later, you can try to plan a route in the area, and then proactively send the scheduler a lower offer,
The other posters have offered excellent advice. Their methods of coming up with their numbers may be different, but they have determined what works best for them and I suspect the final results are often similar. What works best for you in the long run depends on your own circumstances.