You say bluetooth will work. Will I be able to send a command from an arduino to another? Say press a button on one arduino and on the other arduino have an lcd screen say "hello there" and when the button is pressed have it say "please come again"?
The vital advantage for you is that this sort of thing can be done with cheap radios. The fundamental purpose of Bluetooth devices is that they will only correspond with devices that they have been specifically paired with, regardless of other chit-chat in the neighbourhood. When I asked about this a year ago, I got a studied and deafening silence on this forum. It is now clear that this can be done - Arduino to Arduino.
Talking in terms of the cheapo JY-MCU modules, the main requirement is that at least one is a master, the HC-05.
comprehensive detail is here
and there has been stuff on this forum but I cannot find it. Cantin's work is notable in that his two Arduinos connect automatically, and he specifically alludes to the JY-MCU module, no expensive shields required(!)
Reflecting on my previous, I now realise that the setup procedure can be expedited by the producer (you) in that whatever you are trying to produce is distributed with the pairing names and/or passwords pre-loaded - no user input required..
Having said all that, I have yet to do this myself, but I have different purposes anyway. Being discouraged by the lack of response on this, I looked at using NRF24 but moved to using a WiFi repeater instead, thereby using only one Arduino. I just use bluetooth to send data to the phone.