I too have had this problem periodically, and it has just occurred again. Trying to repair the .Net installation hasn't fixed the problem this time.
I have pin-pointed the cause of the problem to .Net Windows Updates - I always automatically download updates, but manually install them, so it was quite easy to spot the pattern.
The latest update to .Net breaks the system and causes the "Can't find bass.dll" error.
The update(s) that caused the problem is KB2840628 or KB2836939 or both together.
As I said, doing a repair doesn't solve the problem this time, but removing these updates and restarting does. This is repeatable.
Looks like there is a problem with updates to the .Net framework.
Since KB2840628 is a security update I would really like to be able to install this, but I don't want to lose the games that will be broken by it.
Is there a fix for this issue?
Update
The game has run several times without any issues this evening - just tried it again and got the "Can't find bass.dll" error.
No Windows Updates have been added or removed, and no new software has been added to the PC.
Repairing .Net and restarting resolved the issue this time.
What's going on here?!