Went there at the end of May, 2014. Getting there wasn't hard but it is no longer an easy bus ride.
From Tainan, you have to take a train North to Xinying. Then you cross the street to the bus terminal and take the Yellow bus or one of the local buses to BeiHe. From BeiHe, it's a short bus ride to the lower and upper village in Guangziling. The locals were very helpful directing us, and we got there easily enough.
We stayed a night at King's Garden Villa and got to use the facility there for free with the stay. There was a discount on the room since it was low season. That said, you could just go there to use the spa and hotsprings and be fine. The shower rooms were amazing, and they had towels, swim caps and blow dryers. Next time we would stay at a cheaper place and just use the King Villa facilities as a guest.
The hot springs themselves were great. There were around a dozen different spring pools. Not all of them were the mud water, so there was variety. They had free tubs of mud for you the slather on yourself too. The water is not muddy itself, but just a murky silver color from the mineral deposits. It's probably best to prepare yourself for that so you aren't disappointed. We had a great time though, and would definitely consider going back! If you are in Taiwan for more than a week, it's definitely worth doing, and if you're coming over on a western budget I'd just suggest renting a taxi from Chiayi train station instead of going the bus route.
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