When my first baby was born, bus was my only mode of transport during the week (as dh worked the other side of town, and it was not economical to drive him to work and pick up again, just so I could have the car) I normally only went out one - 2 days a week, and it was normally only ever one bus each way sort of thing. I have even been on the bus a couple of times with my son who is now nearly 4 and my baby daughter who is 4 months. I just put the baby in the front pouch and then had hands free to get the pram on the bus. (however as for carrying shopping, it is not easy so try not to take too much with me LOL)

If the baby is one year old, try and get an umbrella stroller, those cheapish ones from Target or somewhere, I bought one for $30.00 and it lasted heaps longer than the $200.00+ pram I got from Babyco (That didn't really last long and we needed to buy another for our daughter) I usually found that I could get pram on the bus, with the baby in the other arm. As for all the stuff you have to carry, use a backpack. Is your partner going to be on the bus with you? If so it should be easier.