Trying to replace hand grips on a 1999 Royal enfield bullet, having a hard time with throttle side. The plastic throttle piece will not come off existing handlebars

Sounds like the throttle lock is possibly binding up. Remove the right grip. There should be a little half moon shaped piece of plastic in there at the bottom of the switch housing. This plastic piece will have a small hole in the outside edge. This hole has to be placed over the pointed end of the throttle stop. The throttle stop is the plastic star wheel on the outside of the bottom of the right switch housing. There is a small metal Jesus clip on the inside of the switch housing. This clip is supposed to hold the stop from being turned completely out of the switch housing. It's possible the clip came off and is wedged in there.

The best place, in my mind for info like that is the UK Royal Enfield Works;
www.hitchcocksmotocycles.com

You can't find better advice for Royal Enfield.

Idle jet in carb may be blocked. Carb will have to be dismantled and cleaned out.