Mike,
Jack's suggestion of using rail power is a good one, no need to worry about AC. But if you do want to use AC, you don't really need a bridge rectifier to run an LED from AC power. It's better, but not necessary. I have done it many times and, because the LED is a diode anyway, it will run on AC and not be polarity sensitive. The LED will provide half-wave rectification which is all you need. If you are using AC accessory power, like 18 volts, use about a 3K ohm resistor in series with the LED. What happens is the diode blocks the current in one direction and gives you a DC pulse that is higher than the 18 volts, but the LED can handle it since it is on for only 50% of the time. That's OK since it happens 60 (or 50) times a second and you won't notice any flicker. If you do notice a flicker, than you can either go with a full-wave bridge like Jack suggested, or put a capacitor across the LED.