Use a bore brush, with some fine( 4-0) steel wool wrapped around it, to polish the bore. See if that won't get out the " rough spots.
After using the steel wool, I will use the same bore brush, and a cleaning patch( 3 inch square) or two over the brush( the bristles hold onto the patch(es), and put Pearl Drops Tooth paste on to further polish the bore. Mostly, this procedure only polished the hands, and the edges of the grooves. Often, particularly on new barrels, the roughness you feel are burrs on the edges of the grooves, and those can be removed with steel wool, and polished as I have described. Light rust on the lands will come off with the steel wool, too.
Some people use very light loads- just enough to get the ball out the gun-- to shoot PRB with the patch loaded with toothpaste, or more coarse lapping compounds, purchased at Auto parts stores. That is a fast way to clean the gun opf rust, and polish the lands. Provided, you then follow through with giving the bore a thorough cleaning with soap and water. Then dry the barrel and use a good oil, or a product made for storing guns for any length of time.
As long as the last 8 inches of your barrel are in good shape, the little rust you are finding further down should not affect the accuracy of the barrel.