Your reader almost certainly needs to be connected via USB.
You will need to make sure that you have your Wine set up to 'see' USB devices (sorry I can't help with details on that).
Does the device show up in Windows Explorer as a drive under Wine?
If not, ADE almost certainly won't work with it.
Is the device a Sony? If so, you need a special driver to have it seen by ADE, even on a 'real' Windows, and even if it shows as a drive under explorer.
The only way I know to get that driver is to install Sony Reader (even if you don't actually use Sony Reader itself).
It may be worth trying the older version of ADE.
The new one is full of bugs and doesn't work properly on XP; it may well not work properly under Wine.
There are lots of bugs in ADE2.0. Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172