To add to the line 20 problem -
I'm running into the same thing - wordpress 2.6, bbpress 1.0.
I don't have a lot of time to sort through it, but with a little testing tonight, here's what I found out - hopefully someone can take this and run with it:
The problem occurs initially in the function bb_is_installed(), but that function is not the problem - somehow, $bbdb is getting unset somewhere. If you remove the call to bb_is_installed(), as ck suggested, you just get the error the next time it calls for $bbdb (I think line 1796, Im not sure what function).
$bbdb is set properly right up to the point where bb_is_installed() is called.
Calling bb-load.php directly from bbsynch.php works fine, as long as the call does not come from within a function. As soon as you try to call it from inside a function, $bbdb stops working again. It sounds like a scope problem to me, but apparently my knowledge of scope in php is lacking, because I just can't figure out what is going wrong.
Looking forward to a solution, this plugin sounds great!