"Assume that there is a setup with Bob which creates some sort of interference of the qubits he receives."
I think you need to be more specific on this point. From Bob's perspective his qubit is simply a mixed state in the computational basis
so he will not be able to perceive any ...
Bob does not "see" the interference in the sense you assume. To "see" the interference (actually the states of his qubits) Bob needs to measure the qubits, and the measurement gives Bob no information whether Alice measured her qubits or not.