Bursa is easily accessible by ferry and/or bus from Istanbul, making it worth a day trip or two to see. I used the Moovit app to navigate the public transportation system, for which you can use a contactless credit card to pay for. The sights in the city center are easy to walk from one to another, but if you want to go to the village of Cumalikizik you will need to use transportation. There are minibuses and city buses you can use -- note that minibuses can't be found online (ask around to find them) and you will need to pay in cash. I used the city buses, though, and it worked out just fine.
Cumalikizik is very tourist-forward and has a bunch of stalls for buying different souvenirs, if that's something you would like to do. There are also hotels you can stay the night at, although I didn't feel it was necessary. The village is a popular breakfast spot. I would reccommend getting to try "karadut suyu" (black mulberry juice) from a local seller, it was really delicious! In the village, there is a small museum (no English signage) that is free of charge. I found it interesting, so I would recommend coming with a translate app if you don't speak Turkish. Additionally, there is a house you can enter (Küpeli Ev) for a price of 60 liras in February 2025. You have to pay in cash.