Sorry I'm a bit late on this.
In short: I'm not "very" familiar with Adobe Bridge. When I've implemented "XMP: DateTime copy from EXIF" (into GUI), it was after trying out Adobe Lightroom -which had some DateTime bugs at that time. This GUI option copies three DateTime tags into XMP:
EXIF:DateTimeOriginal into XMP:DateTimeOriginal
EXIF:CreateDate into XMP:DateTimeDigitized
EXIF:ModifyDate into XMP:ModifyDate
-at that time, only these three tags existed (and as mentioned, caused troubles inside Lightroom).
As XMP can contain almost anything, there might be more than three DateTime tags (serving different purposes). And going further, new DateTime tags might be added in future. Speaking for me (off topic): only EXIF DateTime values matter.
Now, as far I know (after trying out Adobe Photoshop), you should be able to modify various XMP DateTime values using Adobe software (Bridge?). Have you tried?
Anyway, I'm quite sure, using Exiftoot "pure", you can edit any existing XMP DateTime tag.
Could you name the XMP tag you wish to modify (and from which EXIF tag you wish value to be copied)?