No you don't have to keep the cover on while bleeding. You also don't want to leave the cover off for a long period of time, off while bleeding is okay. Brake fluid will absorb moisture and that leads to rust in the system. It also lowers the boiling point of the fluid. Boiling the fluid is not likely to happen unless you're working the brakes really hard, like in pro-touring or towing a heavy load but if it does it's not a good thing. I'm not even sure if that happens with drum brakes but it can with disc brakes.
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Hank
70 Chevelle SS396(454), M20, 3.73
My Chevelle
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