I am assuming that this is not a collectible with tremendous value--if so consult a specialist in restorations.
Try a product called Blue Wonder--it is a gel and designed to remove rust from a bore. You might also get some Kroil which is a light penetrating oil and a bit better in my estimation than PB Blaster (which can also work). Both blue wonder and kroil can work together using one after the other in an alternating fashion. Between applications, you scrub with something like bronze or copper wool wrapped around a bore brush (remove the rust particles after each stroke from the bore and wool as much as possible with mineral spirits as these can scratch) and repeat. After removing the rust, a product called jb bore shine which is a jewelers polishing paste essentially, can be used to polish the bore.
It is tedious but well within an average person's ability. Just be aware that it will not cure pitting as if the rust has penetrated to a certain extent, removing it will leave pits which unfortunately is the way of the world. Leaving it alone is worse.