It should take you only about 15minutes max, i take this train everyday to this stop. Good Luck! :)
Once an Orange Line train arrives if your connection with the Red Line is immediate about 8 minutes. Any waiting for a Red Line train will be additional.But if you are going to South Station to catch Amtrak south or one of about 80% of the south side commuter rail trains you need not go there; just stay of the Orange Line until Back Bay Station.
Here s the Orange Line schedulehttp://www.mbta.com/templates/popup.asp?��North Station to Back Bay Station is only 6 stops on the 18-stop line.http://www.mbta.com/schedules_and_maps/s��
Probably about 20 minutes, but if it s an important appointment, allow yourself twice that so you can get there early.use www.mbta.org and click on subway for a trip planner.