Cable car to Uludağ
The narrow (wide enough for vehicles to pass side by side though) and tarmac road from Bursa (with signs pointing it all around the city) winds on the side of the mountain for 22 km until it arrives at the national park gate at Karabelen. After the gate, it turns into—or rather isn't upgraded from since it was opened—a cobbled road, presumably to force drivers to lower their speed, so that driving under icy conditions in winter on this winding road is safe. The cobbled road lasts for 8 km until Sarıalan, or 12 km until Oteller (area where all hotels are clustered).
In winter, vehicles without tire chains may not be allowed to go further than park gate if park authorities decide so (which usually do so in heavily-snowing days). Fortunately, you'll see a lot of stalls run by local people on sides of the road which sell chains—though they'll for sure try to rip you off if it's one of those no-cars-without-chains days (like trying to sell the chain for up to 100 TL, whereas it would cost about 15 TL elsewhere). Whether a snowy day or not, winter drivingrules apply.
30-person cable cars (teleferik) from Bursa's upper neighbourhood of Teferrüç on the foothills of the mountain (minibuses with signs Teferrüç – Teleferik get there from central Bursa) take a much more direct route than the road. It takes around 20-25 minutes to get to the Sarıalan station located at 1,634 mt above the sea level. At about mid-way up to Sarıalan, there is a change station at Kadıyayla. Because of space constraints, no skiing/snowboarding equipment is allowed in the cable car, but fortunately you can rent them up on the mountain. As of 2010, teleferik ride from Teferrüç to Sarıalan costs 10 TL pp return on Wednesdays and Fridays, 15 TL pp return on other days. Children aged 7-12 are entitled for a 50% concession. Departures start 8:30AM with 30-minute intervals until 10AM. Then, there is a departure every 40 minutes during the rest of the day with the last departure from Teferrüç to Sarıalan at 8PM and the last returning departure to the city at 8:20PM Cable car service may be cancelled due to bad weather, especially in wintertime.
If that's the case, then you can take 15-person minibus (called dolmuş in Turkish) from Bursa, which have no fixed hours, and depart when full. Their departure stop is in Tophane, next to the Saltanatkapı gate of old city walls. It takes around 50 minutes to get to Oteller (area where all hotels are clustered), their last stop in Uludağ, by these dolmuşes and a one-way trip costs 9 TL pp. There are also dolmuş taksis with a capacity of four passengers available, which naturally have less waiting times until they are full, and which cost 15 TL pp one-way.