A roundtrip taxi should cost just under 100 euros. You can ask the driver (or have your hotel call and ask) as you get into the taxi while in Ponta Delgada to pick you up in Furnas at a specific time. Otherwise you can simply ask the front desk in the hotel in Furnas, adjacent to the park, to call a taxi for you.
Furnas village is stunning and warrants an entire day, and overnight if possible. I suggest at least three hours or so to enjoy the thermal pools and walk through the park and gardens. A must-do is eating cozido at one of the restaurants in the village or in Terra Nostra Garden Hotel.
I strongly suggest not taking a bus. Sure, you will save a ton of money, but it will be a long and slow journey to get there and back. Allow well over 90 minutes and over 50 stops each way. The bus stops in Furnas are outside the park entrance or very close to it. There might only be three buses per day, in either direction, depending on the day of the week.
Lots of companies offer day trips and you should still have time to explore the village on your own if you desire. Check TripAdvisor for reviews. Otherwise, depending on what month you will be there, a rental car will be economical, allow you to sightsee on the way to Furnas and on the way back, and be a big time saver.
Please know the first 52 pages of my Azores guidebook are totally free to access and read. The link is in the post written by the webmaster at the top of this Portugal forum. By the way, I designed a full day self-guided walking tour of Furnas that is in the Sao Miguel chapter.
I hope this helps. :-)