Assume the following setup:

1. User bob is working locally on his workstation foo.


2. User alice is working locally on her workstation bar.


3. User bob has ssh access to server baz:22 via a key stored at bob@foo:.ssh/id_rsa.


4. User alice has ssh access to bob's workstation foo:22 but not to server baz.

Is there a way for bob to ssh to baz sharing his session (via port forwarding?) or key (via ssh-agent forwarding?) such that alice can access baz from bar via foo (assuming bob's identity on foo)?

Addendum:

There are a few mor thinks that I should have clarfied:

1. 
   bob doesn't want alice to know his password


2. 
   bob doesn't want alice to be able to run rm -rf /home/bob on foo (on baz however that would be fine obbviously).

As suggested by @mukesh-sai-kumar,
one could have alice login to foo (as bob?) and ssh with the shared key from there.

The best approach I can see so far would be to create a new key-pair for alice on bar, allow the public key on foo and automatically run the ssh bob@baz via the command="ssh [...]" option in the authorized_keys file.

This would allow to setup ssh baz on bar to actually ssh bob@foo using the new key-pair via alice@bar:.ssh/config with the forwarding of bob@foo logins using this specific key to bob@baz via bob@foo:.ssh/authorized_keys (authorizing alice's key but restricting command to the ssh baz call).

This way, the two new constraints would be met and alice wouldn't even see anything as this hypothetical interactive session shows:

[alice@foo:~] (1) $ hostname

foo    

[alice@foo:~] (2) $ whoami

alice

[alice@foo:~] (3) $ ssh baz

[bob@baz:~] (1) $ hostname

baz    

[bob@baz:~] (2) $ whoami

bob

[bob@baz:~] (3) $ exit

[alice@foo:~] (4) $ hostname

foo    

[alice@foo:~] (5) $ whoami

alice

[alice@foo:~] (6) $

The only remaining problem is that bob's ssh key on foo needs to be shared with bob's session initated by the ssh from alice (via ssh-agent?) .

Alice can give Bob her public key, and Bob can add a line to his own .ssh/authorized_keys file that will allow Alice to start a ssh session (as Bob) on Bob's workstation foo. Using the command= option, Bob can restrict Alice's key to not grant an interactive shell, but a nested ssh connection to baz as Bob, and using a key locally accessible to Bob on bar.

command="ssh -I .ssh/id_rsa bob@baz:22" ssh-rsa AAA...== alice@whatever

Optionally, you can include further constraint options (no-port-forwarding, from=, etc. - see sshd man page section on AUTHORIZED_KEYS FILE FORMAT).

When Alice runs ssh bob@bar and authenticates with her private key, she will be connected through bar to a ssh session on baz, without having any control over the intermediate session on Bob's workstation.

Note that from the perspective of baz (logging, security audit), there is no distinction between this tunneled connection initiated by Alice, and a "normal" connection by Bob from his own workstation. This may be what you asked for, but not what you want.

For making the protected key available to Alice for her session, you can explicitly set the environment variable SSH_AUTH_SOCK to be the path that Bob uses for his session (change the authorized_keys entry to command="SSH_AUTH_SOCK=/path/to/bobs/agent_socket ssh bob@baz:22" ssh-rsa AAA...) To avoid having to update the path when it changes (logoff/login typically), Bob can run a dedicated agent on Alice's behalf with an explicit path specified (ssh-agent -a ~/.ssh/agent_for_alice and add only the specific key with SSH_AUTH_SOCK=~/.ssh/agent_for_alice ssh-add ~/.ssh/id_rsa and entering the passphrase.

Solution: Nested SSH session.

alice may log into bob's workstation (foo:22) via SSH with the identity of bob, and then log into baz via SSH with bob's identity (and his key, as they both are now accessible to alice).

A command-based representation of this:

alice@bar:~$ ssh bob@foo

bob@foo's password:

---snip----

bob@foo:~$ ssh -i /home/bob/.ssh/id_rsa (your-user)@baz

----RSA ID based authentication----

your-user@baz:~$

Diagrammatical representation:

alice@bar -> Log into foo as user bob -> use bob's stored key to log into baz -> Achieved!