There are a variety of ways on how to go to Bali from Yogyakarta. You could commute to Probolinggo and take the ferry to Bali or alternatively you could book a package thru one of the travel agencies in Yogyakarta which I find very convenient.
Average cost that I saw was around 230-250,000 Rupiah.
Alternatively, you could book a Mt. Bromo tour that would take you all the way to Denpasar which we did.
Average cost of this trip was around 330-350,000 Rupiah. It includes van from Yogyakarta to your hostel in Cemoro Lawang, overnight stay in hostel, breakfast and transport to Denpasar (or back to Yogyakarta).
If you want a transport to the viewpoint and to the foot of Mt. Bromo, you’ll have to pay an additional fee. I booked my tour thru Cecko Tours that can be found in Gang II in Malioboro. We never had a problem except that the van that we used broke down a couple of times. Good thing that we’re not following any schedule so we didn’t bother at all.
The Mt. Bromo tour starts at 4am to see the sunrise at 5am. The view was really spectacular, I almost didn’t go because I was lazy to wake up. Good thing I did because it’s one of the most beautiful things I’ve ever seen.
We left Yoschi Hotel at around 11:30AM en route to Denpasar and arrived at Denpasar City at around 9:30PM. Instead of looking and transferring to another taxi, we just opted to pay the driver additional 50,000 Rupiah (per person) to take us straight to Ubud.
Alternatively, you can take a taxi from Denpasar to Ubud instead and it might be cheaper especially if you’re travelling in a group of three or four.
For more recommendations view my Indonesia travel guide.