You can look up the resistance per unit length for various gauges of nichrome wire. You divide the voltage (Volts) by the resistance (Ohms) to get current (Amps) and you multiply the current (Amps) times the voltage (Volts) to get wattage (Watts).
At 110 Volts if you have a 110 Ohm heater it will draw 1 Amp and produce 110 Watts of heat. If your heater is 220 Ohms it will draw 1/2 Amp and produce 55 Watts.
The hard part will be determining how many Watts of heat you need. That will depend on how quickly the heat transfers away from the stuff being heated. That will depend on surface area and air flow. You have not said how big your bed is or how well insulated it is.
You can make the resistance lower by making the heating wire shorter. You should over-estimate the length of heating wire you need and then cut it shorter if you need more heat to reach the desired temperature.
The wire has to be well insulated (electrically) from the aluminum. If the wire gets to hot it will burn through the Kapton, short against the aluminum and either cause a shock hazard for massive sparks and fire hazard.