Is there a way to show the complete ssh and su chain in bash?

For example. In Server A as user aa:

su - ab
ssh ba@B
su - bb

Thus, I would like a command that prints something like this:

1 bash aa in A
2 su ab in A
3 ssh ba in B
4 su bb in B

I tried pstree but it does not print the users and only works with the processes of the last ssh'ed server:

$ pstree | grep -C 5 pstree
serversshd---sshd---sshd---bash---su---bash-+-grep
     |                                       `-pstree

Thanks and regards.