We have a light fixture in the bathroom which takes 120V G6.35 halogen pin-style bulbs. Is there a XENON bulb in 120V in this size, and would it be compatible?
My apologies, but I must revise my original answer.
There are "xenon" bulbs that are actually halogen bulbs filled with xenon gas. But what many consider to be a xenon bulb is an HID bulb filled with xenon. You must have a ballast associated with an HID light (halogens are not HID, there are no ballasts).
I cannot find a 120V xenon halogens with a G6.35 base, either. I do see several 12V and 24V xenon halogen bulbs (OSRAM HLX); but otherwise, 120V xenon halogens have G8 bases (I don't think that OSRAM even has a G8 base; OSRAM does has a G8.5 base).
Since a xenon halogen bulb is generally lower wattage and has a lower operating temperature than halogen, you could probably retrofit the halogen lamp (if you absolutely love or need the lamp housing and are willing to go the extra mile to convert it to xenon) without needing to worry about the housing burning up. In such a case, I would recommend ordering a G8 base to retrofit your halogen lamp housing (but definitely make sure the xenon bulb that you purchase has a lower wattage than your current halogen, just to be safe). Also you need to make sure the G8 base can fit into your lamp housing, and that you are able to swap bases in your lamp housing. You should probably write a note inside the cover of the lamp regarding the change, including what was taken out... or better yet the actual specifications.
I also wonder about the alternative possibility of adding a transformer to convert 120V to 24V. Again you would need to pay attention to the wattage, especially with respect to an added transformer. For example, OSRAMS EHJ 64655 HLX bulb is a 10,000 lumen, 250 watt (10.4? amps x 24 V) bulb that might leave you blind and start a fire.
The real deal with halogen (incandescent bulbs) is that 99% of the gas is either argon, xenon, or krypton or a blend; and only 1% is actually halogen (usually iodine). The effect of using 99% xenon instead of argon is a minor improvement to the quality. In this case however, xenon is a little better than krypton or argon. Sometimes the manufacturer will use xenon and not even bother mentioning it (except in the technical data sheets like OSRAM's - Xenophot® technology (HLX)), while other manufacturers will outright claim that they have a xenon bulb (and paint it blue, and increase the cost- it's sales pitch).
On the other hand, it is also fair to admit that a xenon HID bulb is actually just a metal halide usually (mercury) in xenon gas.