Welcome from South Carolina!
It sounds like you are doing well and have the right attitude. You can very likely outshoot a lot of us right now.
What caliber is your AR10? What length barrel? What ammo or bullet are you using? And what optics? I have a 7.62 x 51 and 6.5 Creed in AR 10. Both have 20" barrels.
I surely hate that you may not be able to get the Bergara. It bothers me immensely that laws may keep someone from getting the equipment they need for this sport. Particularly a bolt action rifle for goodness sakes. Especially a lady because we need more just like you on our side. Hopefully something will change or some type of mircle happens to allow you to get what you want.