I fly aboutr 10-15 times a year, always have at least one pistol with me with plenty of mags and ammo, never had any issue whatsoever. They always search your bag which I find hilarious but I've never had anyone get upset or 'scared'.
Only issue I might have had was in Alaska of all places, not really a big deal though; they did not search my bag and I asked them to go ahead and search it so I didn't get hassled later. The lady said, no, it didn't need searched. I almost made it through security and my name was called over the PA. I got pissed but then the TSA just took my combo's for my locks and did the search allowing me to stay thru security. They just wanted to verify that the ammo was properly packed.
People just assume you're going on a hunting trip or something, never seems to raise any eyebrows.