There is no such option. If you are seeing this message, then some addon you are using is severely broken, and is generating so many errors that it is slowing down your whole game. I don't understand why you would be opposed to fixing or replacing an addon that is just broken.
If you're using a UI pack, then your addons are probably not actually up to date. I've seen packs containing a version of my addon from over a year before the pack was uploaded.
Anyway, if you're not going to post the name of the addon that's triggering such a huge number of errors, or at least the name of the UI pack you're using, then you will need to figure out how to modify the !BugGrabber source code. Since this is a horrible idea, I'm not going to help you do it.
I'm going to stress what Phanx said again, but you will probably still just not care ...
That message only pops up if there are so many errors being thrown BugGrabber gives up on catching them. As the message states, there are more than 20 per second. That addon is severely broken and is slowing down your game. Good luck with raids, BGs, etc. with a fps drop like that. Your addon may not even be working at all.
If they run so smoothly and you just don't want to see the error messages I have a better suggestion just for you
1. Uninstall both BugGrabber and BugSack.
2. Escape, Interface, Game, Help, uncheck "Display Lua Errors".
3. Ignorance is bliss,
you'll never be bothered by errors again and you just got rid of 2 useless addons.
A "useless" addon is by definition one that doesn't do what the poster wants it to do, regardless of any other considerations.
Ya know, I'm really tired of hearing those damn sirens every time I get on the highway. I'm perfectly capable of driving at 100 mph, I don't know why the cops have a problem with it. I know! I'll get some earplugs! Then I don't have to listen to the sirens!
A better analogy in this case would be something about using earplugs to avoid hearing the termites eating the wood inside your walls. :p
Also, it's rather rude to come say "I have an addon that's broken" in an addon developer community, but refuse to even say which addon. I'm sure its author doesn't want their addon to be broken and spamming users with errors, but if it only breaks under certain circumstances, they probably have no idea, and will never be able to fix it unless someone tells them about it.