calculating the size of a heating resistor
Your calculations are correct and no, for generating heat there's no need to rectify anything. Short form of power is \$ P = \frac{u^2}R \$ so in other words \$\frac{120^2}{3000} = 4.8W\$ which is what you wanted.

That being said, connecting live wires to an exposed resistor is dangerous, do you have skill/background to make a robust connection that's not going to let the wires come loose etc? 5V power supply wires shorted creates sparks and possibly smoke depending on the power supply, loose live wires can create a dead hobbyist.

A much safer alternative would be to get 5V or 12V power supply and use that to generate the heat. You don't need to get a single chunky resistor either, you can daisy chain cheap 1W or 2W resistors with reasonable derating (say, 50%) to achieve the same heating. Solder them to a breadboard for extra robustness. 

Do not use breadboard for live circuits unless you really know what you're doing and have everything inside insulated case with cable strain reliefs et al.