İ agree with Geordie Nev..the cheapest way is to go by local bus..or te ferry and bus.
Buses in turkey are very cheap and efficient.
İ dont know how much it is from İstanbul to Bursa but since its just a couple of hours then expect to pay about 15 /20 lira...if you take the ferry route that will also be cheap.
Hi..I just came from Bursa to Istanbul. I paid 18 tl using the Metro Bus. It's the same vice versa as I went back a couple weeks ago. I was going to Gorukle (near Uludag Univ.) from Otogar bus station in Istanbul.