To save time going through a complicated explination on the course I always find it best to watch some of the videos people have posted (there are many links on the video files/proof page off the SMK records site).  Try to mimic the paths they take and then find a path that works for you.  I usually try to master one part of the course at a time.  Each time you perfect a new corner you are rewarded with a better time.

BC3 is a very annoying course, the simple fact is most races are impossible to complete without crashing because of the thwomps.  You just have to be persistent and keep at it until you get lucky really.  Don't take any risks and just try to get round without losing speed, and try not to get too frustrated when the thwomps are being annoying!
As for which lane to take, I don't think it makes a big difference.  I usually take the inside lane but if there is only a small gap through the thwomps it's sometimes easier to go for the middle lane as you get away with turning later that way.
Hope this helps and good luck,
Matt. (no:1 hater of BC3!!)