Pumping the fuel control (throttle) does nothing to an stopped engine. What you may have heard is to crank the engine with the STOP pulled. But that doesn't sound useful. On engines with electric pumps you might bleed by running the electric pump
without cranking. Sometimes this is done with the PREHEAT switch. But preheat should be limited to 30 seconds per minute (see manual).
If you opened a bleed valve while pumping the manual pump and nothing came out then it sounds like a problem with the pump. Or no fuel. Sometimes the manual pump doesn't pump because the engine driven part of it already has the diaphragm
depressed. Bump the engine a small bit with the starter and see if it then pumps.
A Beta 20, if it's like one I have, should bleed itself in a minute of pumping, even without loosening a bleed screw.