It is the fourth largest city in Turkey with a population of 2.6 million people.
It is beneath Mount Uludağ, a popular ski resort.
Take the Bursaray metro to Küçük Sanayi and walk around until you find a suitable place to hitch.
It is fairly easy to hitchhike to Bursa from Izmir or Istanbul. Yalova is just north and there are ferries to there if you are feeling too lazy to hitch around Izmit. There is more information on ferries and hitchhiking from Istanbul on the Eskihisar page. The cheapest ferry seems to be from Pendik in Istanbul. You cannot hitchhike the Istanbul-Bursa car ferry.
The bus system and Bursaray metro system costs 2TL for a single ticket. A card can be bought for 3.50TL or you can borrow one. With a card it costs 1.25TL, and can be used for more than one person at a time. Each station has a security guard with a metal detector and it seems quite difficult to blackride unless you are super sneaky.