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Bob: That sounds like Bohmian mechanics, which is distinct from either of the interpretations Eliezer has been talking about.
As I understand it, interpretations with actual wavefunctions and collapse still just describe the universe by the wavefunction, it's just that collapse keeps the wave function bunched up so the world can usually be approximately described by a single configuration.
Eliezer: You still calculate the whole wave function, so it's hardly local, and can therefore be a deterministic hidden variable theory that agrees with experiment. I think you just compute an amplitude current from the wave function, and say that the real world or your test particles follow that velocity field in configuration space.
Pretty pictures at http://bohm-mechanics.uibk.ac.at/index.htm