In some ways it makes sense to install the dependencies in Shotgun’s Python, e.g. C:\Program Files\Shotgun\Python3\Lib\site-packages on Windows. One issue is that you need to be Administrator to write in this directory by default.
One random idea - have a look at ./install/core/python/tank/commands/cache_apps.py (which downloads ShotGrid bundles, defined in the env config). Potentially you can add your own command to install all dependencies. It would be nice if the bundle can itself declare what dependencies it needs installed.
Edit: just saw this other thread that has tons of related info. There are tk-cpenv, shotgun-rez, etc.