Ways to Get Around Shanghai

Jim has a driver, whose English name is Jack. He speaks very little English, but we manage. His job is basically to drive Jim or me wherever we want and wait for us. He drives a Honda Oddysey, which is comfortable and safe. That's important because traffic in Shanghai is INSANE.
I remember as a child seeing photos of China and throngs of people on bicycles. There are still a lot of bikes, but in the past 16 years private citizens have been allowed to own cars. That means the crowded roads are full of people with 16 or fewer years of experience behind the wheel. Drivers seem to have an intolerance for any uncovered pavement. It's normal for 4 cars to be squished into 3 lanes, and there is a constant jostling. It would all move more smoothly if everyone was content to stay in their lane and go forward, but no. Add to that all sort of contraptions along the sides of the road -bikes, electric bikes, scooters, small motorcycles, and a certain kind of bicycle I don't know how to name. It's 3-wheeled with a bed on the back, oftentimes loaded to defy physics. Sometimes it has a plastic tent to act as a rickshaw. i've seen it rigged with some kind of benches to hold 4 people, enclosed with plywood and plastic. I thought it was homemade, but then I saw a few others. I guess they could be the product of one entrepreneur. I still haven't figured out the rules at intersections. Everyone, on/in whatever vehicle seem to just turn in front of each other with no regard to safety. This morning I rode to Cooper Tire with Jim and people were running across the road near the plant amidst the crazy traffic. Even though no one was actually bouncing off one another it reminded me of Brownian motion. I'm grateful that Jack has excellent reaction time and chutzpah.
I don't like the idea of being so dependent on Jack. I have a card on me with the address of Jim's apartment, so I could get a taxi if I had to. Buses look too grimy for me. I think I'll eventually get comfortable with the subway system. In the meantime Jack has instructions from Jim not to lose me.