Password to password mapping
The simplest solution to this would be to encrypt Bob's pass phrase under Alice's pass phrase.

In particular the following steps would be carried out for that:


Generate a salted password hash (using e.g. Argon2 or bcrypt) from Alice's pass phrase, call it $SK$
Use $SK$ to encrypt Bob's pass phrase symmetrically, e.g. using AES-GCM


If you want to be fancy and allow Bob to update his pass phrase you can also symmetrically encrypt a private asymmetric key in step 2 and use the corresponding public key to encrypt the new pass phrase whenever Bob updates it.

This can also be integrated into the standard password-hash based authentication flow by using a fast hash (like a SHA256) of $SK$ as the stored database hash value.