And in spite of widespread public support for that individual right...
Are you trying to say that there exists public support for opposing any sort of gun regulation, or that the majority of the public supports it? The second thing isn't true at all, it's just that the minority who really care about guns really care about guns and are single issue voters. The broader public which supports gun regulation doesn't consider it to be more important than other issues.
There is widespread public support for all of the individual rights explicitly pointed out in the Bill of Rights, including the right to bear arms. The level of support varies among individuals (apparently for some people speech is a low priority, since they are supporting a Constitutional amendment to weaken it), but in general they are all supported.
As far as arms rights, most people want to keep arms away from proven bad actors (convicted violent felons), so Bloomberg has convinced a significant portion of low information voters that there is some loophole that allows them easy access. Of course, most people would like to pass on their family-owned firearms to the progeny without requesting permission to do so from federal bureaucrats, so I don't think his disarmament proposals are going to get very far, even in comparatively liberal Washington state.