You should be able to install Bluefire reader app and register it with the same Adobe ID that you use for ADE. You can then copy books (using file manager or similar, not ADE) to the tablet and read them using Bluefire.
If the books aren't DRM no need to use ADE at all.
If the books are library books, Bluefire will work as above. Alternatively, if it is more convenient for you, you can use the Overdrive app on the tablet to borrow, download and read books without needing PC/Mac or ADE at all.