If you go to
http://www.mbta.com, there's a trip planning tool that you may find helpful.
If you're arriving without checked luggage, I would think transferring via Back Bay and the Orange Line would probably be easier than taking a bus, though an MBTA bus would save some tiny amount of money (less than $1) vs taking the subway. The subway probably runs more frequently and more reliably than a bus.
If you have a lot of time and really want to see South Station, you could also take the Red Line from South Station and transfer to either the Orange Line (at Downtown Crossing) or the Green Line (at Park Street), though some of the northbound trains at Park Street probably won't continue all the way to North Station. I would be kind of surprised if there's a bus that runs frequently enough and on a reliable enough schedule for the bus to be faster than taking two subway trains, and transferring from one subway train to another is free.
Whether you take a bus or the subway, you get a discount if you use a contact-less CharlieCard (not to be confused with the magnetic stripe CharlieTicket). The bus fareboxes will take exact change (or can issue a CharlieTicket with any change if you put in dollar bills), and the subway vending machines will issue a CharlieTicket if you don't have anything, but the best approach is to load a CharlieCard with enough value at a subway station vending machine. (I think there are also CharlieTicket vending machines in the large hall at South Station next to the commuter rail tracks, because that's how they want you to buy commuter rail tickets these days.) I'm not sure if there's any reliable way for someone coming from out of town to get a CharlieCard, but there usually is an MBTA employee at the fare gates at each subway station, and if you see such an employee it doesn't hurt to ask if they have a CharlieCard they can give you (there shouldn't be any charge to get one).