After doing a quick search there doesn't seem to be any very good prices to BGO. If nor you or anyone else can find a good deal then I would recommend you to go to Oslo and then take one of the cheap flights available OSL-BGO. Or maybe the train? Trainfares start at $21 in 2nd class or $32 in comfort class for this scenic 7-hour ride!
I have been doing a lot of research on how to get to Bergen since I'm going there next month. Just have to find the cheapest way from HEL first though and a lot is sold out...