It will be a little tricky getting the bbPress plugin working again, but it is possible. You will need to understand how PHP arrays are stored in a database, and manipulate an existing array to add the bbPress plugin.
In the table wp_options, look for record where option_name='active_plugins' and backup the value for that record (I just store the text in notepad).
Next, make your change. In this extremely simple example, you would want to change "a:3" to "a:4", and before the last curly brace add i:3; ... then determine the length of the string for the bbPress plugin main php file (sorry I'm not very familiar with bbPress) and add the last line similar to the others.
a:3:{
i:0;
s:29:"gravityforms/gravityforms.php";
i:1;
s:21:"pagemash/pagemash.php";
i:2;
s:52:"testimonials-by-woothemes/woothemes-testimonials.php";
}
When you save the value to the database, make sure there is no whitespace. This SHOULD get yoru bbPress plugin back up and running.
As for the root of your problem, my guess is that there is a dashboard widget or another plugin that is tied to permissions that bbPress set up, and when bbPress was removed it removed what was being looked for.