The Laurel Mountain solution does a great job with rust blueing! Make sure you follow the directions to the letter, you can get them off their website.
Yes, you need to use distilled water--tap or well water may have chemical traces that will discolor the blue (I have learned this the hard way.....). I have had good success with Walmart distilled water. I have a sheet steel tank with a homemade pipe burner I boil my barrels in, but I have heard of gutter being used successfully. I have not tried scalding the barrel with boiling water (as LMF instructions state), or steaming-- but there are videos on YouTube that show this.
I think a common mistake is carding the barrel too hard after heating, especially if you are using degreased steel wool. It is easy to take too much oxide off the the edges of the barrel flats and get them back down to bare steel. Go lightly and remember you are only trying to remove loose oxide, not polish the steel. After the last carding I put the barrel into a bath of new motor oil for 2-3 days.