Ok, I called them. No, you don't need to stay 3 hours. You can finish in 1.5-2 hours, according to the guy I talked to. I checked the website again and there're 17 steps. The recommended times for steps 1-15 add to 97 minutes. Steps 16-17 are rest periods of one hour each.

Thanks again!

For those wondering, I ended up spending about one hour at the spa. Layout was a little confusing. But no, you don't have to spend 3 hours there.

Bus 201 takes you into the city (2 euros). I got off at Leopoldplatz. There's a route posted in the bus. I had no idea where I was going, but I had a small map of the city center and I just guessed.