Traffic stops to my knownledge do not bring up that you CCW as I have been stopped on the rare occasion and they have asked me if I was carrying, CT is not a duty to inform state but if they ask be honest and be able to show your permit. They usually ask if you have a weapon when getting your information so they would know prior to running you.
The only thing I suggest to do differently is if you have to go near the gun to get your information (glovebox) notify the LEO that you are carrying and have a permit and show him your permit, DO NOT say you have a gun its the best way I know to be face down roadside at gun point. I carry my wallet on my strong side so if I am pulled over I get my wallet out before the LEO gets to the car, never had an issue.
As far as an off duty LEO assking you about a bulge I never seen, heard of it happening or had it happen to me. They most likely not be concerned about the person with a bulge if you are not looking like a ragga-muffin like anyone else it could be anything cellphone, pda. If you are printing or he sees it that may be something all together different. If they do not identify him or herself as LEO then as far as I am concerned they are not and don't just ask to see a badge any one can get a badge ask for their LEO photo ID they all have them.