The Gjendesheim cabin does not open until mid June and the buses do not operate in the off-peak season. I don't know when you are planning to go in September, but I would expect the buses to stop operating around mid September. Time tables for this summer are not available yet.
Since the Norwegian Railways and many bus companies operate with demand-based pricing, it is difficult to compare prices without having a specific date to search for. Since the bus timetables are not available yet, you will also not be able to search for exact prices until you can select a specific departure.
Your price search for railway tickets is incorrect. Norwegian Railways offer saver fares starting at 249 NOK for any distance in Norway. At least with some luck and ordering well in advance, you can get train tickets from Bergen to Otta as well for 249 NOK.
Going from Oslo, the fastest and cheapest option is probably to take the Valdres-Ekspressen bus directly from Oslo via Fagernes to Gjendesheim. The bus will take about 4.5 hours and I would expect tickets to start somewhere between 300 and 350 NOK, perhaps even less if you are lucky.
Going from Bergen, the train via Otta is a substantial detour. Taking the bus from Bergen via Fagernes to Gjendesheim will take about 8 hours with prices starting around 600 NOK.
If you are open for other destinations than Gjendesheim, there are of course many other locations you can use as an entry point to the national park or the Jotunheimen area in general, but you have to expect that public transport is scarce in the most remote areas, if available at all.