You have a couple of options.
Soak the area well with automatic tranny fluid and keep it wet. ATF cuts rust well.
One technique I have used is to get a worn out bronze brush and put a couple of wraps of 4/0 steel wool on it. Oil it well and polish the rust out. Make sure the brush is worn out so if you need to reverse the direction of the brush you can while it is still in the bore. Being that your rust is near the muzzle you want to go very lightly, the muzzle is where the accuracy of the rifle is. Dont make any more passes out of the muzzle than is needed to clean up the rust. Some people will use JB bore paste but I personally think it is a bit too abrasive.

The other option is through an electro chemical process that is used on heavily leaded/coppered bores. It will work with rust but you need to be careful as the solution can damage the blueing.

If it is just light surface rust it should clean up without being detrimental to the accuracy of the rifle. If it is pitted then the only true fix is to cut the barrel back and re-crown.

Feel free to PM me if you need any help with it.