Masada and Ein Gedi in a day

Welcome to Thorn Tree.

Your problem is fitting everything in with closing times, not so much the buses or the amount of daylight (in mid-May it gets dark around 8 o'clock.

Both Masada and Ein Gedi nature reserve close at 5 p.m. in summer (April to September), and the first bus from Jerusalem is at 8:30 a.m., arriving at Ein Gedi around 10, so you are not going to be anywhere before the crowds arrive. This doesn't give you a huge amount of time or flexibility to play with. Of course you can't do it on either a Friday (last bus back will be too early) or Saturday (no buses).

I would be inclined to do the Ein Gedi hike first, for safety reasons. You don't want to find yourself in some fairly remote location up in the nature reserve around closing time. I don't know whether the people selling tickets at the gate will go around just before closing time rounding everybody up... and what if you're miles away then? You could find yourself locked in for the night! This wouldn't be a problem at Masada, where everything is concentrated in a smaller area.

Consider staying overnight at either Ein Gedi or Masada. There are hostels at both places.

As for crowds, mid week shouldn't be too crowded unless you're unfortunate enough to be stuck behind a school field trip... That said, if you want a secluded desert experience (as I would), you should be there at 08:00 when they open the gate.
If you want to get a full day's experience, either rent a car the previous day in Jerusalem and head out at around 06:40 in the morning or as Shuffaluff suggested, sleep at either location.
Between the two, I would begin with Ein Gedi because there are some narrow trails and bottle necks so if it is crowded, you'll feel it, as opposed to Masada where people spread around the site.
One last consideration, May temps. are fine but if there's exceptionally warm weather, consider the fact that Masada it totally exposed and better done early in the day, especially if you intend to hike up.
Have fun.

In case you do it by bus, here are the current mid week schedules:
Jerusalem - Ein Gedi
http://mslworld.egged.co.il/EggedTimeTable/WebForms/wfrmMain.aspx?width=1024&language=en&company=1&state=#
Ein Gedi - Masada
http://mslworld.egged.co.il/EggedTimeTable/WebForms/wfrmMain.aspx?width=1024&language=en&company=1&state=#
Masada - Jerusalem
http://mslworld.egged.co.il/EggedTimeTable/WebForms/wfrmMain.aspx?width=1024&language=en&company=1&state=#

one way to do this and get an early start would be to take the last afternoon bus from jerusalem and stay at either the ein gedi or matzada hostel, wherever you want to be first, and then enter the site as it opens at 8 the next morning.