An easier way then a bore scope, cheaper, handier, and more functional in the long run. If you have an O'Reilly Auto Parts store in your area, they sell a very slim pocket clip model flashlight. The clip comes off. Its an LED and VERY BRIGHT! What I do is take the clip off, then gently side that super thin flashlight, beam on and facing the muzzle to the bottom of the breech. This light will allow you a detailed clear lighted view of the bore of the barrel. To see into the breech itself, hold the light at the top of the muzzle and shine down into the barrel. Or roll a very small piece of aluminum foil into a ball, drop that down the barrel and hit it with a light. The foil will reflect the light and allow you to see the breech of your rifle. It will light all the way to the bottom and again, you can see and check the barrel. Its not a bore scope. But its multi functional, has batteries that can be replaced, and it cost $10.00 and tax. Many flash lights are too thick to fit in barrels. This one fits my .45 calibers and up, with ease.
Be careful you will find that light very useful around the house too as its small, bright and clips inside your pocket. I own three of them. It seems I am always looking for something in a dark place, and or working on something that I need light on but no way to hang light. Mouths work great for holding the tiny flashlight.
I have even used it in early morning hours to light my way to a deer stand or put my boat in the water at one of our back country lakes. Just a handy thing to have IMO.