you don't really have to run very fast at all to push start a bike. just enough to overcome the resistence from the clutch.
on my vespa grande, sometimes i just sit on it and push on the ground w/ my feet (more walking than running) and it starts up. and that's after sitting a full day or two.
on minarelli or puch or similar mopeds, you can just stand next to the bike, take a quick 2-3 steps, pull the starter lever, and usually by the time you jump on the seat and let go of the clutch, it's already fired up. if i'm in a hurry, i push start my bike (like chasing some moped thieves). it takes a bit more energy than the relaxed pedal-start, but its quicker and you get more top speed sooner. dan always run starts his mopeds before racing them.
a well-tuned bike w/ a good clutch cable will start up push starting w/in a 3-4 yards.
also ... you can push start:
mopeds with verona, califo engines