I've been doing reflected UV using a modified mirrorless, micro four-thirds camera, which allows you to focus in live view without having to refocus when you capture the images. I use a small, 1-watt UV-LED flashlight as both a focusing aid and as the UV-A radiation source for reflected UV imaging. I use a relatively inexpensive Noflexar Novoflex 35mm f/3.5 macro, which has good UV transmission properties because of its lack of UV coatings. Here are links to information about this lens as well as other specialized lens options on Dr. Klaus Schmidt's UV photography and macro lens websites (for which I'm relying on his prior permission to cite):
Some versions of this lens reportedly perform better than others in the UV and it's worth checking before buying. [Disclosure: I purchased my Noflexar macro from Dr. Schmidt.] But they're much less expensive than the apochromatic lenses and allow UV imaging with reasonable exposure times (10-30 sec on my camera, usually). As George points out, you'll still get some focus shift using this lens when you compare IR and visible images to the UV image. For stacking and image registration, there are several options (Photoshop, CHI's Imalign tool, and others).
I agree with George that the Baader Venus filter is the best for UV reflectance. I find I get better contrast with shorter exposures using the Baader filter. The Baader filter is expensive and delicate; you can also use a variety of combinations of UV-pass + IR-blocking filters, which have varying performance, such as those discussed here:
It's important to block any IR component in the UV source to get good UV reflectance images, because silicon CCD and CMOS sensors are more sensitive in the IR than in the UV, so even a small amount of IR leakage will ruin the UV image. Since the Baader filter is so effective at blocking IR, you can even use daylight or any source of UV-A with the Baader filter if you give adequate consideration to the sensitivity of the object to UV, but this might not be a concern with skeletal remains. Wear UV-protective plastic glasses to protect your eyes from UV-A (they're inexpensive and easily available). There are several sources for how to process the images; probably the best source is the AIC Guide.
For UV-induced visible fluorescence that Dale suggested, you'll need a dark room with little to no ambient visible light; a good UV + IR cutoff filter (visible bandpass filter) such as a Hoya IR/UV cutoff filter; and a clean source of UV radiation with no visible blue component. This usually requires filtering the UV source, even if it says "365 nm LED" or such. These LEDs nearly always have a blue tail that extends to wavelengths around 400-410 nm, which interferes with the induced visible fluorescence and degrades the images. I put a Hoya U-340 filter on the UV-LED flashlight to reduce the blue tail, which gives me a peak wavelength of 371 nm and near-zero blue tail.
For UV reflectance and UV-induced fluorescence using the flashlight, I use a long exposure (usually between 10 and 30 sec at around f/5.6 to f/11) and sweep the flashlight beam across the surface to get an even exposure. I might do this 3-4 times and choose the best image. Because you're capturing lots of images and good, even exposure is critical for photogrammetry, this technique won't work for photogrammetry. So you'll probably want to get a stronger UV source or a pair of sources that you can leave stationary relative to the object. Strong sources of UV-A with good filtration to remove the blue tail tend to either cost a lot or they're bulky and awkward to handle, which is why you may want to follow George's suggestion of modifying strobes. I've attempted this but found they didn't produce enough UV-A for my needs, a topic for another discussion.
The trick to getting good UV-induced visible fluorescence images is good filtration on the UV source to eliminate the visible blue tail; good filtration on the lens to cutoff the UV source and any stray IR (only if you're using a modified full-spectrum camera); plus a dark room to reduce stray ambient light. However, at least it doesn't require a modified camera or a special lens, and it has other benefits as Dale suggested.
Because UV-C has shorter wavelengths, it has special optical properties that are useful, but you can't capture UV-C reflectance images using any consumer camera with a silicon-based sensor. You need both special optics and a camera with a specialized sensor to capture UV-C reflectance, and as George mentioned, UV-C is dangerous to work with. You absolutely need to wear protective eyewear and cover skin, and do due diligence. However, you can capture UV-C induced visible fluorescence with an unmodified consumer camera if you put the right filtration on both the source of UV-C and the lens (to eliminate any visible components of the UV source or stray ambient light). These topics are also covered in the AIC Guide and elsewhere.