Rey, in future it's a good idea to include that fact (India, RH drive) at very beginning, so save time of advisors trying to work out solutions that prove irrelevant. MIght consider in future taking some practice in other.. my husband & I tried it in England, starting on country roads, being very cautious, it worked OK. But then it was not mountainous, which greece is.
As for visiting sites by local bus, yes you CAN visit Mycenae by bus, and also Epidaurus. The problem is, only ONE site per day, because the bus schedules don't permit more. These 2 are in Opposite directions. You get a 9:30 bus to Mycenae for instance, and let's say there is a bus back to Nafplio at about 1. You get there at 1:30, but there are no more busses for day to Epidaurus. Samedeal: We did Epidaurus on a 9:30 bus, the bus back was 1:30, no other site visits possible. You could work it to visit an ancient, and later in the day explore nonsites.. such as walks around town. Your additional problem is, you're going in October. In high season, these sites are open longer, and are supposed to be open longer until end of October. However, you may find that they close at 3 -- to be safe, u need to have your hotel check by PHONE. (YOU should have the phone numbers from internet to provide to hotel clerk). NOTE: a few years back, a couple of Nafplio travel agencies used to offer a day-trip to both these, with a iicensed guide along. Somehow, Nafplio tourism does not have its act together! These day-tours have disappeared.
I do have one inspiration for you -- by Googling "Nafplio-based travel agency" I found a link to Argolidlife -- which gives links to licensed guides in the area. Here is the webpage of one: http://www.argolidalife.gr/επαγγελματικός-κατάλογος/υπηρεσίες/Διζέ-Σμαραγδή The text is in English. She guides people around the city of Nafplio (Nauplion) but ALSO puts together day-trips that could combine for example MYCENAE & the theatre of EPIDAURUS. You might write her direct, and ask what it would cost to rend a van seating 5 tourists + driver + her as licensed guide and see those 2 sites. I am afraid it would be costly ... but that is the difficulty for you, in visiting a country which unlike Italy is not easy to access by train, and which has sites widely separated. This is a reason that many people in your situation go on group tours.
If you decide to skip something it should be Meteora ... very time-consuming to get there and at least in my opinion, unless you are deeply into Greek Orthodox and monasteries, it's mainly about buildings on top of really high, really skinny rock-points. I rented a video from the library about it and enjoyed it a lot, from the comfort of my couch!