Remote login must be turned on, or some add-on app must accept commands on a listening port. Third party apps include LANDesk, LanRev, or even ARD (not technically an add-on, since the agent is included with the OS.

If remote login is enabled on B, then ssh <an_admin_username>@B
enter the password for that admin username, then type the command to perform.

I find it easier to put a loginhook and/or a logouthook on the machine, then no remote login needs to occur from then on.

The -hook files contain the path to the script to perform if logname is the name in question, else exit. If you've logged in remotely, you'll need to grep the output of "who" for the username you are looking for.

defaults write /Library/Preferences/com.apple.loginwindow LoginHook /path/to/script

defaults write /Library/Preferences/com.apple.loginwindow LogoutHook /path/to/script

Then, no matter whether you are there to issue a command remotely or not, the scripts can run whenever the target username logs in.

If you need to remove the login or logout hooks:
defaults delete /Library/Preferences/com.apple.loginwindow LoginHook
and/or
defaults delete /Library/Preferences/com.apple.loginwindow LogoutHook

You could delete the scripts too, but without the hooks calling them, they are basically just text files with commands. /path/to/script is generally somewhere users don't mess with. I use /usr/local/sbin/, myself.