To the extent that your bus pass is for shops I suspect you could. But if you would buy the bus pass even without shops, I wouldn't.
Lets give you examples. I have no regular job. I use the bus once a week to go to the grocery store. My bus fare for the round trip would be $2 or $8 for the month. A bus pass costs $20 so it is cheaper for me to pay for the individual trips. As a shopper I use the bus 18 times per month for shops, which would cost me $36 in round trips so I puchase a bus pass for $20. That pass I would claim and not worry about making as many personal trips as desired using the pass.
I buy a bus pass every month to go to work at my regular job. I work M-F except holidays. Weekends I do shops by bus and sometimes I get on and off the bus on my way to or from work to do shops. I would not claim the pass because its primary purpose is commuting to work.
I work 2 days a week, which costs me $16 per month and would not normally buy a pass. With mystery shopping I go out on shops 2 days per week by bus. I would feel comfortable splitting the cost of the bus pass 50/50 between work and shops. If I am mystery shopping 3 or more days per week I would just claim the bus pass because the individual trips would exceed the cost of the pass.
My thinking here is that "commuting" is not a deductible expense. Where mileage comes into the picture, those with a regular job and shops need to be very careful that they don't overlap "commuting" miles with independent contractor miles.
Of course the cost of the bus pass versus individual trips is something you need to use real numbers for to determine. I just picked round numbers for an example and I know they are low even for my area. In general, though, if your mystery shopping trips use cost would exceed the monthly pass cost, then you should be okay.