I used the route recommended in a YouTube video I stumbled on--boat (from either Yenikapi or Pendik in Istanbul) across the Sea of Marmara to either Yalova or Mudanya, then the bus to a Metro Station on the west side of Bursa, then the Metro into the center. The only tricky part was buying the stored-value card required to use city transit in Bursa. Maybe you can now use a tappable credit card.
There are also buses from Istanbul, but I think they also leave you an annoying distance from the city center.
I'm traveling now and don't have access to my notes from that 2023 trip (thus my uncertainty about the exact route I used), but I think I spent about 5 nights in Bursa; I like to spend a lot of time just walking around the cities I visit. For me Bursa's top sight was the UNESCO-listed Muradiye tomb complex. I thought those tombs were more beautiful than the mosques in Istanbul.
I spent about 20 days in Istanbul. It has endless, fascinating sightseeing opportunities