1) If mystery shopping is your only job, you claim mileage door to door. In my driveway I note the mileage out. When I return I note the mileage on return. The difference between the two is my 'business mileage' assuming that I haven't sidetracked for personal errands from a reasonable route to the shop location.
2) If mystery shopping is not your only job, you cannot claim mileage to your normal place of work (that is 'commute mileage') and should check irs.gov for the specifics about 'commute mileage' and 'business mileage' as they may apply to you.