I've answered this so many times, I've finally come up with an all-purpose answer (see below). I will preface it by saying I did a 1-day tour bus on my first Greece trip 18 years ago & hated it ... then finally in May 2012 I believe, I did a d-i-y overnight (see description below) ... wonderful experience. BTW Athens hotels are VERY used to people "skipping" 1 nite for short tours. But if you can't or won't do that, here's my 1-day DIY strategy:
ONE DAY D-I-Y TRIP
First KTEL (intercity) bus is 7:30 AM(2.5hrs); take 4pm or 6:50pm back. Cost pp €30.20 Rd Trip Bus. Taxi from Ath hotel to/from Liossion KTEL terminal €12 each way; DElphi Site admission €12. BUS SCHED: https://www.ktel-fokidas.gr/en/delphi
PLUSSES vs group - Shorter travel time, arrive 45-60mins before crowds; not forced to leave for group lunch
MINUSSES - Early rising for 1-Day trip & must do your own advance prep & onsite self-guiding.
TRAVEL STRATEGY -
The 7:30 bus CAN sell out; formerly could NOT buy a ticket ahead online. Even now, unsure. Have your Hotel Call & do it for you. If not possible, taxi to Station(20 mins) by 6:30am & you'll be OK. (Do NOT attempt local bus!) Terminal has coffee bars, but if planning picnic, buy stuff the night before near hotel. BUS: All seats numbered - Ask for LH side of bus (less sun). All seats reserved; Get a round-trip ticket; specify last bus back (18:15) then if you decide to go earlier, u can exchange in Delphi (see below). Take care of restroom needs at yr hotel (station restrooms r Grim). However Bus has brief rest stop midway. For day trip, Use a Light day-bag or backpack; you'll be carrying it the whole time.
SITE STRATEGY -
At Delphi by about 10am, bus stops right at Museum/Ruins --you have an hour of quiet before tour-bus crowds. You might do ruins first, then when throngs invade, you hit the museum before they pour in @ 12:30 and jampack it. Then with your lunch you walk 500 yards down the road to Tholos & Castalian Springs for a serene picnic; Fill your bottles with pure mountain water!! After tour crowds depart (mostly by 2 or so), you may be able to re-enter ruins site (check earlier with gate staff). Awaiting your own return bus, you needn't stay by the site; actual final "turnaround" stop is uphill on main street, by a souvenir store. Walk uphill along parapet, gazing down mountainside, there's a nice cafe terrace directly across the street for refreshment with a view (local water, in pitchers, sraight from top of Mt. Parnassus, is Nectar of the Gods!).
IF STAYING OVERNIGHT
Same bus & taxi costs staying overnight. With more time, it’s nice to take the 3 pm bus arrive 6 20, stay on til final stop. IF going May-Oct, Museum is open until 8 pm. In this case right after bus arrives walk a few yards & check into a hotel (I recommend PAN hotel, the back rooms look DOWN the mountain to the sea, costs about €35-40 rm; reserve ahead in June-Sept). From hotel walk downhill along parapet to the museum; u can easily see it in an hour, (Very well signaged) then have dinner. Next AM, get to ruins gate by 8 am and youll have 2-3 hours before bus tours swarm in. Return bus sked to Athens varies, sometmes 1,
MY DELPHI LINKS for ADVANCE PREP & PRINT to TAKE:
• Printable Maps! (Museum, Sacred Precinct, more) – http://www.planetware.com/map/delphi-map-gr-del.htm
• Sacred Destinations - http://www.sacred-destinations.com/greece/delphi Ads, but good info; see menu on side
• http://www.ancient-greece.org/archaeology/delphi-archaeology.html
• Dr J's Delphi – http://people.hsc.edu/drjclassics/sites/delphi/sacredway.shtm
NOTE: click items in SIDE MENU for complete photos & explanatory text. SUPER!
• Wikipedia entry, succinct & surprisingly good --- http://en.wikipedia.org/wiki/Delphi