See, for me the issue of trust is so germane to this discussion that it typically receives only a cursory consideration. By trust, I mean not simply 'trusting' (or not) that a responsible gun owner will be responsible, but also trusting (or not) that someone can be somewhere without a gun and feel safe.
To me, this really illustrates the centrality of compromise to the entire discussion. Sure, compromise is nothing new, and god knows 'bi-partisanship' is trite these days, but think about it. Pro-concealers don't trust that they can be safe around others without the gun, and anti-concealers don't trust that they can be safe with other people carrying guns.
The issue of 'rights' doesn't really provide an answer, because both sides are concerned with their basic right to life. The 'right' to carry a weapon does not trump the right to feel safe, because it is the route to doing so for the pro crowd, and also the route through which the anti-crowd feels their safety is threatened. Typically, when issues involving a conflict of basic rights occur, it is the more fundamental right that wins. Is life more fundamental than the right to carry at all times?
The bottom line is that the issue involves basic rights on both sides, so the best solution is one that gives as many people what they want. That is a compromise, and I think it is not a horrible imposition on anyone to designate a bar as off limits for firearms.