Elaine, with 3 people, driving is best option. Bus ticket 1 way = 13.50 x 3 = €40 + taxis at either end... and you can get a modest car for €50. Michelin trip plannershows everything -- exact route on map and step-by-step directions, est. driving time, cost in petrol & tolls -- https://www.viamichelin.com/web/Routes Just remember that the driver will need to have an International Driving Permit (no test no hassle, u just stop by you local AA office w. your regular driving license, pay $20 & get a photo, done in 20 minutes. But DO remember also to take along your regular license too).
http://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg is a FAB online map (click & it gets huuuge) of peloponnese shows the exact route all the way from Airport to Nafplio and all the stuff along the way. Michelin does too, but this also shows terrain and tiny details. As map clearly shows, from Airport you are on modern nonstop intercity divided lane highway... not even needing to tap the brakes until after you cross Corinth Canal. No way to get lost or in trouble ... last time we drove this, it was even in a Rainstorm but no fretting.
If for some reason you did take the bus, it would take time to get to bus station (45-55 minutes by taxi, 65 by X93 bus), then catch the Nafplio express (hourly on half-hour, takes 2.5 hours). When you'd get to Nafplio, you might have to taxi to your lodgings depending on location. If you DO decide to use bus, I would still urge you to rent a car for at least 1 day during your nafplio stay, because that would enable you to see 2 or more ancient sites nearby (Epidaurus/Mycenae, Tiryns, Asine) and local beach ... the schedule of local busses is not set up to enable more than 1 of these per day.
PLUS, if you drive you have some extra options -- after the Corinith Canal, you can exit at "Ancient Nemea" and just 5 miles off the highway see the "runner up to Olympia" as a games site .. ancient stadium & all.. PLUS stop at one of the countries best wineries in the local village for Nemean Red (yum!). After Nemea, you just drive across (or under) the biggie road & head south on a small (and low-traffic) 2 lane road to Nafplio. During your Nafplio stay, having a car enables you to go up top of the rock-fortress Palamidi (999 steps!!) by driving, not climbing. And on your route BACK to Athens area, you can hit Epidaurus on the way and go up the Coastal Road to "Isthmia" and hop off to see the famous Corinith Canal (it's not visible from the Intercity New Road), and THEN get on the Big road, toward Athens.