I highly reccomend everybody to come here with public transportation. There are quite a lot of busses at a normal european price level.

From Bergen I recommend taking the express boat to Sogndal. It is great fjord cruise, and cost just a little more than the bus. Runs every day all year, Timetable. Prices; adults 540 nok, students 270 nok 

There are express busses:
From Bergen to Sogndal 6 times a day. 4,5 hr. 365 nok.
From Flåm to Sogndal 6 times day. 1,5 hr. 130 nok. 
From Oslo to Sogndal 4 times a day. 7 hr. 495 nok.
From Otta, Lom to Sogndal 2 times a day (only during high season).  

From Sogndal you take local bus to Solvorn. It runs a few times day, but less in the weekends. 20 min, cost 39 NOK. Ask the bus driver to let you off at Eplet in Solvorn. The village has only 200 habitants and the hostel is impossible not to find. 

I can also pick you up in Sogndal for 100 NOK pro person. Need to be booked one day in advance, tel: + 47 41649469.