If you have a running shell, you will have at least the shell builtins, which include things that will let you list files (echo *) and write out data; you could, in theory, use echo or printf to generate a simple netcat binary, and then use that to restore /bin.

Probably easier to just boot from a USB stick and restore though.

[edit] And of course many systems have useful binaries in /usr/bin due to old hard drives being small.