Hi,
Recommended alloys for bright anodizing are 5357, 5457, 5557, 6463, 7016 and 7029. This is based on primarily on experience with automotive trim using phosphoric-nitric acid bright dips.
From The Surface Treatment and Finishing of Aluminum and Its Alloys, 6th Edn., p. 139 (2001).
Your 2011 results, some good and others frosted, indicate that the bright dip solution parameters are out of control and/or there are microstructural variations in the alloy, e.g., any kind of sizeable segregation. The mention of pH suggests you're using a brightening solution other than the phosphoric-nitric acid type. I suggest getting some technical support from your supplier. They will all run free samples, so submit several candidate alloys.
The microstructures of 2011 and 2024 are described and shown on pages 70 and 74-79 in Aluminum: Properties and Physical Metallurgy (1984). Both alloys have primary solidification intermetallics which cannot be fully solutionized afterwards. Those of 2024 are more complex due to greater alloying, but 2011 also contains lead and bismuth. These free-machining additives solidify last within the dendrite interstices, but can form spheroidal globules if the initial solidification is slow and/or during solutionizing. I haven't bright dipped any Al, but have lots of anodizing experience. Most intermetallics and all foreign inclusions can form anodize defects when their size approaches the anodize thickness, so generally a problem above 1 micron and definitely a problem at 1 mil (0.001”). Good results require 1) clean alloy, 2) rapid initial solidification, 3) lots of deformation (to break up segregation) and 4) tight limits on the solutionizing treatment (especially, not overheating).
I presume that you are only doing a flash anodize, so the coloration due to the Cu isn't noticeable. I will remind you that the anodize on 2xxx alloys is softer and less corrosion resistant than on other alloys.
Hope this helps,
Ken