"Do bonding & antibonding MO superimpose now?"

no.

This discussion is getting off the mark.

The question was

My question is why there are 2 combinations, 1s + 1s & 1s - 1s?

Why not the overlapping of two 1s orbitals either 1s + 1s or 1s - 1s?

(Two waves join together should either constructive interference or destructive interference?)

The schroedinger equation is exactly solvable for atoms. It is also exactly solvable for the simplest molecule H2+. Just as atomic wavefunctions having different numbers of nodes and shapes arise as solutions for the one atom, the analogous thing results as wavefunction solutions for the one eletron under the influence of binuclear H2. There is no linear combinations of atomic orbitals involved.

The linear combination of atomic orbitals (LCAO) is a mathematical method that is used to approximate a solution to the schroedinger equation for molecules. The only reason it's used is because the schroedinger equation gets too complex for molecules (other than H2+) to be solved directly and exactly.

Since LCAO is just a mathematical method that adds and subtracts orbitals, it is not necessarily a representation of what happens dynamically in reality (schroedinger equation is the more ideal representation); ie. when 2 s orbitals of two atoms approach, it makes no intuitive sense, as Winga says, to say they simultaneously add and subtract. What is important is that the end result correctly achieved by LCAO is 2 MOs, which if mathematically added together produce the same space as the original atomic orbitals.

That is the idea behind the LCAO method, to produce the correct end result consisting of bonding/antibonding pairs which are not superimposed in the molecule, but if mathematically superimposed all together, produce the original atomic orbitals. It is a manifestation of the conservation of matter and energy and orbitals.