Well, there is no official support for Wine and I am not an expert on either Wine or BeBook eReader. What may help is if it is possible can expose the mass-storage partition that comes from eReader as a USB mass-storage device to Wine (with its own drive letter). Then Digital Editions may be able to see it and give you an option to authorize it. Post back if you manage to work it out - I am unsure if this is possible without Wine modifications.
Another alternative is to activate your BeBook with Mac or Windows PC (with the same AdobeID). Once you do it, you should be able to simply copy DRM books over to the device and they should just work (however, this will not work with library books - those have to be transferred using Digital Editions).
I'm also on openSUSE 11.1 and tried your suggestion. My Sony PRS 350 has been activated on a windows machine. I just bought a DRM protected book and opened it with Digital Editions (using Wine). The books are stored in "$HOME/My Digital Editions" and can be copied to the reader using any file manager. Works!