My point was that (I believe) you cannot have rights without also taking on the responsibilities that go with those rights. If you do not believe that then yes it is fine to talk just about a Bill of Rights but that would surely also mean that a Bill of Rights would be unworkable? It would be all about "my rights" not the rights of others - which, by virtue of considering them, means "my responsibilities".
Maybe I am alone in this - "Your position does not give you the right to command. It only imposes on you the duty of so living your life that others can accept your commands without being humiliated." Dag Hammarsjkjold. Substitute 'commands' for 'rights' and it seems like a reasonable sort of philosophy to me - or perhaps "Love one another" in the widest sense of "Respect one another" - again it means responsibilities, not just rights.
Do I make sense or do I have it all wrong?

In a Constitution or Bill of Rights, every ‘right’ automatically creates a ‘duty’ or ‘responsibility’. In the first three Rights in the UN Declaration, for example:
1. Everyone has the right to life, liberty and security of person.
2. No one shall be held in slavery or servitude; slavery and the slave trade shall be prohibited in all their forms.
3. No one shall be subjected to torture or to cruel, inhuman or degrading treatment or punishment.

Number 1 automatically creates numbers 2 and 3 and a host of other duties, caveats, and responsibilities. If everyone has the right to life – then murder is automatically forbidden.
If a woman has the ‘right’ to control over her own body, and to determine whether or not she will bear a child, then automatically, contraception and abortion are permitted.
If we all have the right to live in an unpolluted world, then automatically, we have a responsibility to keep the world clean and unpolluted. It is not necessary to enumerate the responsibilities.

That's a very simplistic approach which does not work. There is a need to enumerate responsibilities - not just assume their existence from rights