If by the hashing operation you mean application of the OWP, keep in mind that inverting the OWP is supposed to be hard, and furthermore, since it's a OWP, if A

If by the hashing operation you mean application of the OWP, keep in mind that inverting the OWP is supposed to be hard, and furthermore, since it's a OWP, if Alice and Bob start with different secret keys, they won't hit the same "hash" as the output of the OWP. For this to work, they'd have to start off with the same secret key already, which makes the key exchange pointless. You mention using this approach to slowly grow a secret key, by performing many iterations of this protocol, but if you do it bit-by-bit, the adversary can easily brute force invert the OWP over {0, 1}, and thereby learn the secret key