Two ways to get the fluid flowing. A hand vacuum pump on the bleeder fitting to suck fluid down, or get a small pump oil can. A clean new one, and fill from the caliper up to the reservoir. Start with the reservoir empty. Put DOT 4 fluid in the new can and then dedicate this oiler to nothing but this type fluid. Don't store fluid in the can. Throw away what you don't use. Put some fluid through it first to clean it out even if it is a new pump, just to be sure it is flowing clean. Keep the can full enough that it doesn't start pumping air halfway through the job. Use a clear hose between the pump can and the bleeder so you can watch for any bubbles. You may see a few but they will work their way up to the reservoir. Once the reservoir is full, close the bleeder and try your pedal.
A word on front brakes and clutch bleeding. On certain model bikes with certain design handlebars there are hoses that run up hill and then down to the caliper or clutch piston. You can bleed all day without getting the last bubble out. You need to put the cap back on the reservoir and remove the master cylinder assembly from the handlebar and hold it vertical until the bubble makes its way up into the reservoir.