Your main concern is that when you disconnect the line from the old caliper that the brake fluid will start leaking out. If you take too long to get it bolted up to the replacement caliper, you could drain the reservoir in the Master Cylinder and make the bleeding more of a chore.
You don't have to rush like a madman, but you don't want to make a phone call or go take a leak in the meantime.
After the new caliper is on, top off the Master Cylinder. Loosen the bleeder fitting on the caliper and wait until gravity makes brake fluid leak out. Snug up the bleeder. At this point, it would be nice to have a helper. Someone to pump the brake pedal. A clear piece of plastic tubing that will snugly fit over the nipple on the bleeder will make the job less messy along with a receptacle of some kind to catch the fluid. You can use a wad of paper towels to absorb the fluid and some care and get the job done too.
Crack open the bleeder valve and have your assistant gently press the pedal down. Have your assistant tell you when the pedal reaches its lowest point and then close the bleeder. Have the assistant allow the pedal to raise. When it's at the top have the assistant tell you, open the bleeder and repeat until just fluid and no air comes out. Doing the gravity bleed as you did will just about ensure that all the air is out anyway. The additional bleeding is just to make sure.
Some things to know;
Brake fluid is death on paint. It will take paint off quicker than you can say 'oh shit'. If the brake fluid is dark, consider flushing out the whole system by bleeding at all four corners.