By westerner bit, do you mean a bit that is suitable for the western discipline? How is your horse trained? Does he/she neck rein? How soft is their mouth? What kinds of things do you do with them; showing, trails, cattle work, etc.?
A good way is to ask friends who may have spare bits to let you borrow to try different ones with your horse. If you are buying a new horse it's always good to ask what he goes best in. Keep in mind that sometimes they actually do better in something different. ;)
Case in point, my Granddaugter's horse.. Previous owner said he went great in a TomThumb(western). He actually works great for her in a Kimberwick with a roller in the middle and also goes very nicely in a ported curb bit.