How do I calculate the gas-mileage when riding sharing with a rental?

You don't calculate anything really. If using the actual expenses method (which you can not use if the vehicle is less than 100% business use) you have receipts for everything and just add them up.

If using the per-mile method (as you would with a rental since the vehicle is not 100% business use) you just enter your mileage when asked for it in the Vehicle Expenses section and the program figures it for you.

For the most part though, you will find that claiming vehicle expenses on rental property will not help your tax liability one single penny, and is (in my opinion) an absolute waste of your time and effort, since rental property already operates at a loss on paper.