Older versions of the Online Bible do not run properly on Wine. Versions 3.95 and later run well on Wine and have implemented reference sharing with Bibledit.
A bit of help follows below. It may help you getting the Online Bible running on Linux and getting reference sharing to work.
Install the Online Bible on Linux through wine:
wine install_advance.exe
After installing it, run it as follows:
wine "c:\Program Files\Bible\olb.exe"
Start Bibledit, go to menu Preferences / Reference exchange, and tick the option to send references to the Online Bible.
In Bibledit, menu Preferences / Windows Outpost, enable the Outpost, and when locating Wine, use plain Wine.
That's all what's to it.
When if you change a reference, you will notice that the Online Bible starts, and that its desktop is empty. In the Online Bible, Open a Bible or press F6 to open a desktop, move Bibledit to another verse, and notice that the Online Bible scrolls along with Bibledit.
If Bibledit starts, stops, starts again, then the Online Bible desktop no longer can be restored through F6. The solution to this is not to use the standard "Online Bible Desktop", but to create and use your own.