So should I do a delay before sending "$$$" and then another delay before trying to read the response?
Sounds like the hardware setup is all wrong. OP hasn't described how "anything" is hooked up, but the first guess is he has the RN-XV going to the same pins as the USB port on the Arduino, so that will never ever work. Too much guessing. I hooked up my RN-XV this morning and typed "$$$", and got back "OK" right off. Then, I typed "get e", and it displayed the complete setup.