In truth, the patches will always come out slightly darker color. What you want to avoid is a patch that is dark black in color. Use the light test, not the patch test. Hold the barrel up to a lamp and if you see shiny then you're good to go.
If you don't take any advice from me, just simply remember not to use bronze brushes so much. For example, you clean, get frustrated, run a bronze brush, then get even more frustrated.
Several things to keep in mind:
1) Using solvent with bronze brushes, or jag will give false readings. It's entirely possible to endlessly clean the barrel with a jag and solvent because what is really going on is that the solvent is reacting to the bronze jag and your barrel is actually clean.
2) Using bronze brushes in general gives a dark color patch. It's best to only use the bronze brush in the first pass through and never use it again in the cleaning process. For example, you come one, soak the barrel with solvent patch, then follow it up with bronze brush for 10 passes, then after that only use patches. Don't retry the bronze brush as you will get a endless cycle of black patches.
3) Shiny barrel is a better idea to test. When you get home from the range, look at the barrel in the light. It will look horrible. A clean barrel will be shiny.
4) Try to avoid bronze items through the barrel if your aim is to get a clean patch.
5) Guns don't rust or corrode as fast as you're led to believe. While it is a great idea to clean your firearm as soon as possible, it is not vital or critical that you clean it immediately or else it'll turn into a hunk of pitted metal. Best thing to do is let the gun breathe air. Don't seal it up in a case.
6) Try to avoid switching brands, even for different things. Sometimes the chemical can react but it is very unlikely. Make sure you're using proper cleaners. For example, if you use purely oil to clean the barrel, you might find it to be nearly impossible to clean unless you spend hours with the patches.
7) 15-20 patches sound pretty normal to get it white.
8) Don't believe in commercials on how to clean your rifle. If the video you watch is promoting a product, don't believe anything about how clean something is. Chances are the firearm they got out is set up to be squeaky clean. There's no way to determine how many times they edited the video to get it to look like the way they did.
9) Just remember the number one cause of damage to a gun is during the cleaning process.