Hey Trooper Danzig. I didn't have a scope on my Rem. I only cleaned the bore, and used q-tips to clean the bolt area.
Since this is a Ruger 10/22 forum, I can talk more about how I clean my 10/22. I haven't had mine long, but it is so simple. I use fishing line to pull patches thru the bore. Coyote suguested Weedeater mono, it should be stronger. I clean the bore only most of the time. If I want further cleaning, one screw, and the barrel/receiver comes out. Punch out the trigger group pins, and you can get at everything. Barrel, and Scope stay mounted.