Bottom bracket question
 

I recently got a used 2006 specialized sirrus sport to fix up and im having issues with the shifting. The only thing that nakes sense is that the BB spindle is to short (113mm from the factory) causing poor shifting including the high gear to go so for over that the chain falls off. I have tried setting the limiting screws but it just doesnt cut it. The 2 shift is wsy over as well. Ive also tried other shifters and derailleurs and i kerp voming back to the BB.
looking for input and recommendations

2006 is a pretty old bike. Was it ever right? If it ever worked properly the problem isn't likely to be the bottom bracket.

My advice is to pull up the Park Tool instructions for installing a new front derailleur and to follow them step-by-step IN ORDER from the very beginning without skipping any steps. Don't progress to the next step until you are convinced the previous one is right. I've solved a number of seriously frustrating front derailleur shifting problems. The ultimate cause of most of them has been improper positioning of the derailleur on the seat tube.

If it shifts into the small chainring okay, the BB probably isn't too short. But you can measure the chainline to be sure.

I'll echo the suggestion above--start over. Pay attention to mounting height on the down tube.

It sounds like you're saying the front derailleur will over-shift the tallest chain ring and you can't screw the high limit screw in far enough to effectively limit the derailleur's travel. Is this the case?

You said what the BB is from the factory (113mm), but is that what's on it now? Has the BB been replaced with a shorter one? Or has the front derailleur been replaced with a different model? Or has the crankset been replaced? It's highly unlikely that Specialized built a bike that couldn't be adjusted properly, so I suspect something else may be influencing this. Replacement of any of those front drivetrain components with one with a slightly different specification can throw the balance off.

All you need to do is measure your chainline (and compare it to what it should be for that bike) and you'll know whether the BB is too long or too short. That would be unlikely if it's factory stock, but that's where to start.