Tannic acid will bind to the iron oxide and convert it to ferric tannate. It's used by museum personnel to preserve arrows and ancient steel parts as they're uncovered. It's also one of the main ingredients to most anti-rust products, like evaporust.
http://www.ebay.com/itm/Tannic-Acid-...ht_2659wt_1170
(You could make your own from tea leaves, tree bark, with acetone and a double boiler/distiller, but that seems like a bit of work)
Soak the parts overnight in the tannic acid that's been disolved in distilled water. The finish is fragile, and the deactivated iron will flake off if you brush it with a stiff bristle.
If you wanted to make it more durable for a finish, you would need to add phosphoric acid to the mix, and well as other ingredients to help the ingredients penetrate deeper like wetting agents. Since it's inside your bore, you WANT it to flake off, so I would use some steel wool wrapped around an old worn out brush to knock it off.
You may need to repeat the process if it's got heavy scale to get deeper down, but if it's light just one treatment should work well.
I was thinking of using this with experimentation for rust bluing, but the finish is not durable. But it will really help if you're trying to REMOVE rust.
Using electrolysis will also remove the rust in a non-destructive method. Baking soda and water mix applied as an electrolyte solution with a steel rod wrapped every 4 inches with electrical tape to keep the rod from shorting out. Plug the bore, add solution, energize, wait, and then scrub the rust that deposits on your rod off with a piece of rough steel wool. Repeat until no rust is deposited on your rod. Search for electrolysis rust removal on youtube.
Brownells and midway sell a rust removal system that consists of a battery pack, some wire, and a rod and some "special solution" for 135.00 but I'd rather just use the stuff sitting around my house instead.
Andy