The right to bear arms, which is a constitutional right, was designed to grant people the right to oppose an oppressive government. I suggest that while this reasoning might have been legitimate when it was written into the Constitution, it doesn't look at all realistic today when governments have an incredible stock of armaments that can overcome any gun-carrying population. The operational reasoning is not there. It is more an expression of an ideology than a true solution to a potential problem. Thus, we should reinterpret what this constitutional right should really be.
To me, people who collect, hunt, or use guns for sport should have the right to have guns. It makes total sense. I would suggest that hunters, sportspeople, and collectors should belong to an association of like-minded people. Then, only bonafide members of that association can buy a gun. The ability to grant membership should belong to the association. They know who is a true hunter, sportsperson, or collector. If it is discovered that the member has been involved in using the gun for criminal activity, then the whole association is subject to scrutiny and may even lose their right to grant membership.
I am imitating here the model of micro banking. You can get a loan as long as a whole group of people that know you guarantee your loan, and if you don't pay it back, they lose the right for loans, too. So they must watch out for each other.
What I am proposing is the decentralization of supervision and control of gun sales to associations, to people that know each other better than some central government will screen who can buy and who can not. The more decentralized the system, the closer the people are to where the problem is, the better the control. That's what I believe.