How do you 'burp' the line after replacing the upper radiator hose on a 1997 Cavalier 2.2 with no radiator cap?

Assuming you didn't drain the system, you shouldn't have to burp it at all. Just keep the reservoir full and warm up the engine. it circulates through the reservoir and back to the radiator.

To "bleed" the cooling system on a 1997 Chevy Cavalier, there is a small brass bleeder valve located on the heater pipe that runs along the front of the motor (metal pipe). Open that valve a couple turns and pour in the antifreeze in the reservoir tank until antifreeze starts dripping from the bleeder hole. Tighten the valve, but be careful not to tight too tight, they are soft brass and break easy. Finish filling the reservoir to the Full Cold mark. After driving the car at least one time and letting it cool down, check the antifreeze level on the reservoir and fill as needed.