If you go to Merida you will find quite a number of organized tours to both Uxmal and Ruta Puuc which I think is quite good for older people but if you really want to enjoy these places you can perfectly go by a public bus. There are two bus stations in Merida:ADO and second classes (oriente and Sur).
It takes two hours to get to Uxmal from Merida but you have to take a,so called,second class bus and it will cost you aproximately 5 US dollars for a one way ticket. The bus stops at 200m from the entrance to the site.It is very easy to visit the place since in front of each monument you will find explications both in Spanosh and English but if you really like the world of Mayas,buy a book in the bookshops at the entrance. It will take you 4 hours to explore the ruins and then you can take the bus and go back to Merida but I would advise to spend a night in the hotel overlooking the Magician's temple ("The Lodge at Uxmal"-beautiful relaxing hotel).This way you'll be able to enjoy the Night show and in the morning you can continue your trip to the other Ruta Puuc's monuments.