sometimes while bleeding the brakes solo, I'll open the bleeder just one flat or sometimes two, attach a poly line into a container then start pumping, the resistance of the partially open bleeder gives good backpressure to keep from sucking air back into the caliper. Eight or nine good pumps at each corner usually does the trick. Once you have a good full fluid path, just opening the bleeder with a hose attached will gravity bleed a good steady stream of fluid. The pattern is important esp if you ran the master out of fluid while changing your caliper. Helpful tip, fill the caliper as full as possible before installing it. Gravity bleed your clutch too while keeping the reservoir filled to the tip top.
The pattern LR/RR LF/RF is stressed, previously mentioned and should be followed, longest to shortest fluid path. If you've gotten air in your master, it might take a quart or two to purge it all out.