Sue, we did exactly the same thing a few years ago. Intended going to Patara for the day and ended up on a tour. Enjoyable as it was it wasn't really what we wanted.
However, a couple of years ago we did manage it. We stayed in Patara village for a couple of nights and had a full day on the beach.
You need to go to the main Otogar in Fethiye, not the dolumus station, and make enquiries about a bus to Patara. This will more than likely be the bus to Kas/Kalkan but will stop off at the top of the road into the village of Patara and a dolmus will be waiting to take you down into either the village or the beach.
Coming back just get the dolmus up to the main road again and ask one of the many people who are usually hanging around there for the bus to Fethiye.
If you are going though, it really is worth thinking about spending a night in one the of the hostels/hotels in Patara village, it's so very different to the tourist areas.
Good luck.