To be honest you are better off renting a car. Public transport in rural areas is not so frequent and you might get stuck somewhere.
Muhu is a nice place to visit. Definitely spend some time there.
You can see a fair amount of Saaremaa by bus. I've done Saaremaa and Muhu by bus and hired bikes. This was about the perfect combination if the weather is good. I cycled from Kuressaare via the meteor crater at Kaali and on to Muhu, where I visited Koguva village, which is worth a look, and a nearby emu farm. I took the bike back to Kuressaare by bus.