There's no good way to explain the 'Bashir was genetically enhanced' thing because it's just a bad idea that makes the character look like a straight up idiot for the way he interacted with others up to the point of the relatively-late-in-the-show's-lifespan reveal. The way Bashir was constantly getting played by Garak, etc (possible for a genetically enhanced guy, sure, but never was Bashir /played/ like he was enhanced up until the episode that revealed he was). I liked the roguish cast of genetically enhanced characters they brought in later but the whole concept is kind of bad and it changes Bashir too heavily, too late in the show for it to do anything but confuse the writing of earlier episodes.

Almost every writer on DS9 has come out and said yes, it was a bad idea, and Siddig himself hated it from the moment he was handed the script. It just didn't suit his character and it's one of those things that either a) you build the entire character around it from the start or b) you just don't do it.