I stayed in Parma 3 years ago on a solo trip, and took a food tour from there, which included Parma ham. No rental car, and I later took the train for a few nights in Bologna.
I liked Bologna so much that my husband and I went there this last September for a week, and took a food tour from there - better Parmagiano and balsamic vinegar (and Saba) segments, although the prosciutto portion wasn’t as good as the Parma tour. The tour company provided transportation in a Mercedes van, and the Modena region was part of the route. And the city of Bologna itself - fantastic food experiences without even leaving the city!
We picked up a rental car in Bologna as we headed to other parts of Italy. Based on the brief time exiting Bologna in the car, plus the time spent as pedestrians, if you wanted a car while staying in Bologna, find lodging outside the ring road, where parking is easier, and ZTL’s aren’t a concern. Driving in the very center, as in most major cities in Europe, is not how to spend your vacation.