There are quite a few of these around, it's getting one that will be ok for your baby (eg lie flat) and meet your other criteria. A lot of people buy the Nipper 360 because its easy to push with unbalanced load. Baby jogger also very good (I had one of these for my dts). Can't say I ever went on a bus, don't see much room for singles much less double buggies. And you may well have to fold it, in which case an umbrella fold would work better (although they're often smaller for the child and harder to push) plus a sling for the baby so you can manage it all. Some people use a single buggy plus sling for the bus & have a cheap 3 wheeler for walking etc. it depends on your lifestyle. I found the 3 wheeler I had much easier for negotiating round shops as it turned on a sixpence and kids had enough room as they got older. You can get nippers pretty cheap second hand.
Yes, all but a few side by side doubles will fit through an average doorway but it can be difficult to get them round crowded shops at times. Make sure you measure for your doorway though! I couldn't get a nipper because I had a narrow front door, mountain buggy was only one to fit (expensive still second hand but so fab).