You can easily take Egged Bus #486 which goes often throughout the day, starting at 8:45AM or #421 which leaves Jerusalem at 9:40AM. The #486 leaves from Ein Gedi around 4:12PM and the #487 is the last bus back, leaving Ein Gedi at 6:15PM. But these, I believe, go to and from the Ein Gedi Kibbutz, so ask at the ticket counter if they also go to the SPA (which is in a separate location).
You can also take Egged Bus #444 which leaves Jerusalem at 7AM and 10AM Sun-Thu but when you buy your ticket, be sure to say you want to get off at Ein Gedi SPA (not the kibbutz) so you don't have to pay the full fare and also tell the driver when you get on! You can get the same number bus back but ask at Egged for the times it leaves Eilat and add 2.5 hours and then wait at the bus stop on the road near the spa.
There is lots to do in the area, but remember that the Spa and Kibbutz and Nature Reserve are all in slightly separate areas, but, if you are in good condition, it is possible to walk/hike between them. If you really want to experience all there is to see and do in the area, why not spend one night at the Ein Gedi field school or kibbutz hotel. You can then enjoy the hike through the nature reserve and other activities on that side of the road on one day and spend the next at the spa & floating in the Dead Sea or vice versa!
And don't forget that Qumran is nearby to the north and Masada is nearby to the south!
Hope that information is helpful and whatever you decide, have a GREAT time in Israel!
suzanne pomeranz, tourism consultant
jerusalem, israel - firstname.lastname@example.org