On the basis that a taxi from the Son Baulo hotel to Palma airport would cost you around 70 Euros one-way, I would estimate that the onward journey to Santanyi would take it up to over 100 Euros. So 200 Euros return, for that you could probably hire a small car for 3 days, including petrol. The journey time would be about 1 & 1/2 hours one-way. This assumes the journey is down the motorway to Palma then the ring-road around Palma towards the airport. I can't imagine that it would be any cheaper or quicker taking the backroads down the east coast.
You'll see here...

http://tib.caib.es/terrestre/doc/autobuses/500/502.pdf

...the bus timetable for buses from Palma out to Santanyi. Mon-Frid there's a bus at 11:45am to go and 18:30pm coming back. You could fit this in with buses from/to Alcudia. Lots, lots cheaper, probably around 12 Euros pp one-way.

There is a bus that travels between Can Picafort and Cala Egos. Goes once a week. In the afternoon. On a Saturday. Takes ages. And doesn't come back. And you'd still have to get to Santanyi.

By road, you can take a back road from Son Serra de Marina to Manacor and then on to Felanitx and then Santanyi, but you really need your wits about you. The stretch to Manacor is a bit hairy in parts and not advisable in the dark. It's also easy to get lost especially in Felanitx where the road signs are not obvious. Otherwise you can take the coast road to Arta and then cut down to Porto Cristo and onto Cala D'Or and Santanyi. Ok if you like a scenic route, and time-wise it's about the same as the motorway but Pollensa's absolutely right, the motorway is the easier way of doing it.

The buses to Palma might be an issue as well. The main one that goes via Alcudia (351) starts at the Camping in Can Picafort, so if you're in Son Baulo you'd have to get to it. There is another line (400) that takes a different route entirely but that also starts from the Camping. The only route from Son Baulo (390) involves changing and getting onto a train.