The cathode ray tube in the ESL bulb does not emit X-rays. Unlike in a regular TV tube, the electron beam does not need to be focused. This allows the electron beam to have a lower voltage (about 5000 volts in this case), and so any X-rays produced are much "softer" and easily absorbed by the thick glass. The company did testing, and claims the detectable X-rays are lower than background levels, essentially absolutely nothing to worry about.
I also wanted to add that I cannot use CFL bulbs because they leak out UV radiation and I have a sensitivity to it. It makes my eyes ache and my skin feel sore after about 10-20 minutes of exposure. CFLs work by passing an electric discharge through the mercury vapor inside, producing UV radiation that then makes the phosphor coating glow. But some of this UV leaks out. I seem to be several times more sensitive to CFL bulbs than sunlight, in case you were wondering. Especially if I am sitting close to one, or the room has 5 or 6 spiral CFL bulbs in the room.
Thankfully, the new ESL bulbs do not emit UV radiation, not as far as I know.