Authentication and deniability
In step 2 for Alice, what is the purpose of including Bob's public key in the hash? you can include a timestamp to prevent replay attacks instead.

In step 2 for Bob, there is a typo - should use Alice's public key instead of her private key.

Actually your protocol is similar to PGP, and I dont think it provides deniability because if Bob can prove that the public key belongs to Alice then the owner of the private key is most likely Alice.