Update:Turns out you can do this. See sauoq's reply above. Sorry for the bad info!

I don't think functions are inherited across bash shells like you think they are.

For example, if I type set, I can see a function rs defined in my current shell. If I run /bin/bash --norc from this shell, I no longer see the rs function.

I think that each time bash starts up, it reads the appropriate rc files and re-defines the functions. If that's the case, you could use the BASH_ENV environment variable (see bash(1)) to point to a script containing all of the function definitions.

Another thing worth noting, although it may not be useful in your case: The easiest way to pass information like function definitions back to the shell from Perl is to print the definitions to stdout, then run something like eval `perl script.pl` in the shell.