I'm a bit of a novice about Bridge, but this is what I found (v 14.0):
I don't see that you need this stack feature, as Bridge seems to manage identical twin image files (e.g. myphoto.raw and myphoto.jpeg) in the background as a single "myphoto" without any need for user intervention:
where you load a photo with twin image files (JPEG & RAW) into Bridge and sort the RAW image in the central window, Bridge will manage both these files as a single "photo" (not manage the JPEG and RAW image files separately), so when you finish organising your photo, and move or copy it to another folder, Bridge will automatically include both image files in each "photo" and may add a side-car XMP file [the XMP file contains any tags you added to the RAW file]
so I have been just selecting and working on the RAW files (i.e. just ignoring the JPEG files - keep the JPEG image files hidden from view, and let Bridge manage the house-keeping of these files - if you move them around, Bridge will keep the twin sets of identical JPEG and RAW files together), and at the end of your work when you go to move or copy the RAW file, Bridge will automatically transfer the twin RAW and JPEG image files of each photo together for you
[if in Bridge you view only RAW files in the central window, when you move or copy selected photos to another folder, Bridge will move or copy BOTH the RAW image file (which may now have a sidecar file if you have added a tag) AND its twin JPEG image file;
alternatively, if you view only JPEG files in the central window of Bridge, when you move or copy selected photos to another folder, Bridge will only move or copy the JPEG image file, and will leave the RAW file behind (so if you move the JPEG file, its twin RAW file will become an orphan [which doesn't matter, as you can always recreate the JPEG file from the RAW file by using the function menu: file > export in Bridge]