By ship
Ferries ply the route between Gilimanuk, Bali and Banyuwangi every 20 min, 24 hr a day. The crossing itself takes about 30 min, although embarking and disembarking can take much longer.
Surabaya is a major national and international port city and virtually every major coastal city in Indonesia is connected to it in some way. Check the national passenger ship operator Pelni (http://www.pelni.com/for) detailed information.
By bus
Frequent buses travel across Java and this is a reliable, if not always comfortable, method of travel. All of the the major cities and towns in the region can be reached by bus.
By train
Surabaya is connected by rail from Jakarta, Semarang and Yogyakarta with many stop points in between (http://www.infoka.kereta-...). It is possible to travel to the region from Bali with an all-in "train" ticket that also covers the necessary bus and ferry portions.
The popular star tourist attraction of Bromo-Tengger-Semeru National Park is sadly not part of the Indonesian rail network.