The BBO people have done a bit of work to make it usable on Wine. If you get 4.5.5 beta (or above), it now installs cleanly. After that, you have to edit
C:\Bridge Base Online\bbover.ini
In the [SYSTEM] section, put:
LINUX_WINE=Y
BROWSER_TYPE=A (I was told that E also works, but A works just fine for me)
You also need to find symbol.ttf and put it into C:\Windows\Fonts.
After that, almost everything works. The only things that don't work are the stranger options like speech synthesis, but in terms of playing there is no problem at all.
To get the 4.5.5 beta, go to forums.bridgebase.com and get it from one of the links.