In Greece, the train network is poorly developed. I think you've noticed this if the map you saw is like this one:
https://railsmaps.com/greece
Coming from Bulgaria, you can go to Thessaloniki and take the Thessaloniki-Athens train line.
Afterwards, you'll have to rely on buses. There isn't a single, uniform bus network; the various bus networks are entities called "KTEL something..." that are independent and divided by region. Therefore, you'll need to check the schedules of each KTEL network and see where they share a common bus station (it's no walk in the park!).
Just for the Peloponnese region, if I'm not mistaken, there are 7 different KTEL networks: Korinthias, Argolidas, Arkadias, Lakonias, Messinias, Ileias, and Achaias. To top it all off, there is no way to view a general map of all the KTEL entities and their routes.
Below is a website listing all the KTEL companies along with their individual websites:
https://ktelbus.com/en/category/ktel/
However, since you have two months, I think you'll be able to manage it step by step. In less touristic regions, bus schedules are pretty much identical year-round, the locals always have the same transportation needs no matter the month.
Also keep in mind that, apart from a few locations situated "in town," the vast majority of sites, museums, castles, monasteries, and other places of interest are not accessible by public bus. A map showing some of these locations in the Peloponnese:
https://www.google.com/maps/d/edit?mid=1kFRC74X_9PHcQ_3FNY62F_tURD34mLs&usp=sharing
Just a quick spelling note: it’s Peloponnese, not Pelopennese :-)
