I’d recommend against bluetooth. Bluetooth is a Personal Area Network (PAN), and doesn’t have the kind of range an outdoor application would need. Its official limit is 10 meters (32 feet).
You’d be better off with highly directional antennas (think Pringles can), or even wired. You haven’t given much more in the way of information, but from your Bluetooth question, I assume that you’re somewhat near the display.
If you have access to the electrical power that feeds the display, I’d suggest that you look into some of the products that will send ethernet over the electrical supply. If what you need is purely a display signal (like VGA), then look into one-station IP based KVM switches.
Since you didn’t specify what sort of signal the display actually handles, I can’t do much more than guess about its nature.
Write back with more details.