Judith
You obviously don't drive, or you are not in your 70's or disabled or just find walking hard going or else you would want your car to get you as close as possible to the city. To be honest if it were not for the local trains I would not go near the city now. For me to use Birmingham buses there would have to be a major shake up in the service. I realise that I might be doing Birmingham buses a disservice but I can only go by what I still hear and read about them because I admit my experience of them in recent times is not first hand.
Actually, I do have mobility issues. Walking long distances can be very painful.
I don't drive, but find public transport perfectly adequate. Most bus services service the City Centre. Many stop on Colmore Row, others on Smallbrook Queensway, Moor Street Queensway, Carrs Lane or near Old Square. They stop by the Markets too. You will only have to walk a short distance from any given bus stop to the shops - in fact, most of the bus stops are a lot closer to the main areas than car parks are.
If you were going to Town from Solihull on the 6 or 37 bus for instance, you can get off by the Bull Ring, or stay on & get off outside Boots on the High Street - a few yards from M&S. The closest you'd be able to park to that is Dale End, and the closest station is Moor Street.
The buses no longer go down Corporation Street, but the trams do, so getting about without walking far is relatively easy.