I've just had a quick look at the Bebook website.
http://mybebook.com/ This doesn't mention ADE as one of the supported formats.
It says that supported formats are:
"Supported file formats: pdf, mobi, prc, epub, lit, txt, fb2, doc, html, rtf, djvu, wol, ppt, mbp, chm, bmp, jpg, png, gif, tif, rar, zip, mp3."
and notifies people of an update:
"PDB Support Added - Free update
Surprise surprise! Here's the next free update for your BeBook!
Here's what added in this update:
* The .PDB file format is added.
* The PDF parser is updated to version 7. (
non DRM, but supports password protection)
* The Epub parser is updated. It now supports catelogue/index.
* The CHM parser is updated, it now supports flowing display.
CLICK TO READ AND DOWNLOAD!
Added October 2008"