Bus ticket costs 15.10 euro one way per person, booking a return ticket in Athens booth I think you have slightly discounted fare, say a bit less than 30 euro allez-retour per person. So nearly 90 euro only for the bus Athens to Delphi and v.v., not counting possible taxi or metro fares to get to bus station etc.I am sure a car will cost similar or less for a day.
In temrs of driving conditions, this is up to you really. If you feel comfortable to drive on Naxos and Santorini, I do not see why not to feel comfortable driving the Athens-Delphi route, a good part of the trip is on a modern highway, then in narrow two lane straight road and last 40 kms or so on twisty road and mountain terrain. I know Santorini and NAxos pretty well, and I think if you feel fine driving there, you'll feel fine driving on mainland. You do not mention when this trip is scheduled for, sometimes on winter and even till middle March, occasionaly there might be snow and frost towards Delphi but if you plan to visit on summer, this is irrelevant.
If for whatever reason you do not want to drive and your trip is focused on Delphi sites/museum only, I see not problem using the bus. A car will provide more flexibility though, and why not to exploire a bit the surrounding area, or at least make a small detour to visit Osios Loukas Monastery (an other UNSECO Heritage site) ?

The most difficult part would be driving out of Athens, the rest shouldn't be a problem at all

You could rent a car for 2 days drive to Delphi and stop on your way at Livadia for a coffee break in Kria, a very nice part of the city with a small river, an old water mill and even a gorge at the top of the pedestrianized street( unknown to most Athenians), then make a second stop at the Osios Loukas Monastery ( like Mariha suggested) and after than in the village of Arahova ( you will have to drive through it anyway ).

Delphi is a small village with many hotels, you could overnight there, and explore the archaeological site the next morning, when the tourist busses haven't arrived yet.

Itea and Galaxidi are nearby ( especially the second, which is my favourite town in that area with beautiful old captain houses and great restaurants), so there is plenty to see in the area.