Is there a factor or formula for using a densitometer with a bracketed grey card to get a close approximation for the current ISO?
No simple way that I can see. Here are two things that have to happen when establishing an ISO speed for a general purpose b&w negative film. First you need to develop to a specific "contrast" level (contrast is not exactly correct, but it's fairly close). Second, according to the ISO standard, you need to find an amount of "light energy" that produces a specific small amount of exposure effect on the film. This effect is defined as a density increase of 0.10 above the "clear" base, aka base plus fog. Your densitometer could measure this difference, or you could just say, oh, I see a slight difference from the unexposed part, and this will be pretty close.
The main problem is in knowing the value of that "light energy" that gives the slight "exposure effect." And... the ISO film speed standard does not use exposure meters. However, by looking at both the ISO film speed standard and the ISO exposure meter standard there is a sort of relationship between the two. A member who has studied this sort of thing quite a lot, Stephen Benskin, says that the ISO "speed point," where the film first shows a slight exposure, is defined as being about 3 1/3 f-stops below the exposure meter reading.
So, the suggested method is to 1) find a "correct" development time and temperature, and 2) shoot a series of test exposures that cover a range about 3 to 4 stops below what the meter says. On the developed film you find the frame that is closest to the speed point, meaning that the film is about 0.10 density units above "base plus fog." From your notes (you kept notes, right?) you get the exposure for that frame, then calculate the exposure 3 1/3 stops brighter. This brighter exposure is what the exposure meter is supposed to read. So... adjust the ISO speed on the meter until you get the correct reading. That will give you the correct ISO speed for the film. More or less, anyway. You'll be affected by the precision of setting exposure changes in your camera, as well as any errors in the exposure meter.
Fwiw the gray card's reflectivity doesn't really come into play here. You would get the same result from a white card. This is cuz the meter doesn't know what it's reading. All it knows is the strength of the light it reads, and whatever this is, the meter will attempt to make this record on the film as a mid-gray. And the film speed-point should be 3 1/3 stops down from that point.