Removing Blue... the fastest way that I have seen was a gunsmith had a plastic bucket, gloves, apron, goggles, and a jug of regular Drano. He held the barrel using pliers. In your case, plug the touch hole or the threaded hole for the nipple, and put a cork in the muzzle. Hold the barrel over the bucket muzzle down with a coat hanger through the tang bolt hole in the tang. Pour the Drano straight from the jug onto the barrel and let it flow toward the muzzle and into the bucket. Should take the bluing right off...and then hold the barrel off to the side and rinse with water, followed by lemon juice and water, followed by water. Took about ten minutes when I saw it.
Naval jelly will work too....follow the directions for removing an neutralizing it.
THEN dry and apply the mustard to the barrel as suggested as above. I don't add vinegar to mine. Let the barrel hang and the mustard dry to a brown color and hard. Use a toothbrush and water to scrape off the mustard, then repeat. The vinegar is what is going to "stain" your barrel. You may want several applications, then some folks like to polish the barrel back a bit, some like it as it.
LD