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 (you would have to exit the south side to reach the pedestrian bridge to the gas station westwards or see below about next station).
Alternatively, you can continue on the metro to the last stop, the University, as the stop is situated right on a well lit stretch of highway-and you'd be further along on your way than you would be getting off at an earlier station.
I found upon arriving at this station that the metro continues and turns right blocking your path West to get to the gas station, so you end up walking to the next station Altinsehir and crossing under, adding another 20-25min walk. So you might as well go straight through to there, then walk through the industrial yard. Much closer.
If you are able, find a ride to Minteks Tekstil/Restaurant which is at the merging of the D200 and O-5 increasing your chances. However, there doesn't appear to be any public transport to there, no minibus that I asked would go there.
The road out of town towards Istanbul doesn't have many places where a car can safely pull over so you may have to wait, by turkish standards, a fair amount of time. When you do get picked up you're likely to be given a ride to Gemlik or Orhangazi rather than directly to Istanbul.
One good thing to do is try to get past the highway which runs west to east about 10 km north of town. A lot of traffic comes through this road en-route to Istanbul from cities in the south and if you stand after the intersection your chances of finding a direct ride to Istanbul increases vastly.
Take the metro to the last stop Kestel. From there you are directly at the main road (Ankara Yolu Cd., D200) which takes you east out of the city. A lot of people go to Inegöl from there, but you can also find people who go further.
Alot of traffic coming to Bursa from Istanbul takes the Eskihisar car-ferry to Yalova (the ferry is easily hitchhiked just follow the instructions on the Eskihisar page) It's really easy to just ask around in the ferry for a car going directly to Bursa (atleat 50% of the cars on the ferry go there). Otherwise you could go around the bay of Izmit although it generally takes more time.
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.