I want it to prompt the user for a configuration setting and then save it in a configuration file. What tools/modules will make this easy?

Config::General should suffice.

And what do I have to be careful of?

Not writing enough tests.

What's the best way for the perl module to install this bin script to their machine?

ExtUtils::MakeMaker will handle this.

Is there anyway to avoid requiring the user to have to modify their .bash profile?

Yes - install the binary into an existing entry in the user's $PATH.