Generally, bleeding the brake system requires 2 people but if you have a brake bleeder vacuum pump you can do it yourself. Your description involving removing a line and pumping will introduce air into the system. 2 person brake bleeding is as follows; ensure the brake fluid resrvoir is full of brake fluid; with wheels removed (vehicle safely on jack stands), starting with pass rear, locate bleeder screw on the caliper, have your assistant pump the brake pedal (engine off) till it is hard and HOLD, you crack open the bleed screw and fluid will escape. Your assistant will note when the brake pedal is close to/on the floor (still holding, do not release pedal with bleeder open!) at which time you cinch/tighten bleeder screw closed. Your assistant may release the brake pedal now. You must top off the brake reservoir now to avoid the level getting too low and introducing air into the master cylinder. Should this occur, you may have to take the vehicle (tow time!) to GM and have the abs block "cycled" to remove the air! Repeat as many times as necessary for each wheel to get as much of the old fluid out. Repeat the entire process next with the dr rear, pass fr and last the dr fr caliper. It may be beneficial when doing the last bleeding (each wheel) to tap the caliper body to dislodge any small bullbles that may be clinging to the inner passages. New fluid without air will result in a firmer brake pedal while the engine is running/you are driving. Maybe not a lot but it should be noticeable. A brake pedal that is soft(er) means air was introduced into the system. DO NOT DRIVE. Start the process over until you have a reliably firm pedal.