Here is a repair solution for your Broken throttle shaft for your your Buell X1 all models and years,

Buell S3 1999- up and

Buell XB9 2003 models.

comes with shaft bearings

look here for the Install manual

don't forget to order intake seals 

how to set the TPS on your bike

For Buell XB12 04-07 49mm Throttle Body shaft kit look here