I will be travelling from edinburg to oslo on the 2nd of June (Ryan Air) and flying from Bergen to Paris on 5th (Norwegian). I wanted to know if I should be booking by tour/train to Bergen on the 3rd itself and hence spend an extra day in Bergen or should I travel to Bergen on 4th and hence spend a day in Oslo.
This short visit is not ideal, but it sounds like you're making it a priority to squeeze the fjords and Norway-in-a-Nutshell route into your trip. Oslo has more museums to choose from, so we typically allocate more time there.