Carb needle valve not seating properly, either due to float not floating, not adjusted properly, or needle seat damaged. Adjusting the low speed jet has nothing to do with the seating of the needle valve and sealing fuel off from the carb.
Squeeze bulb puts a lot more pressure on the fuel system in the engine than does fuel pump pressure when running. If you don't believe me, with the engine stopped, squeeze your bulb till it's good and tight....if you can with your leak...if not leaking it would get really firm and would only cosmetically collapse when you squeeze it.
Conversely, feel the bulb when running.......it's soft,not collapsed, but a long way from the resistance you feel when the engine is stopped, aka lot less pressure on the fuel line and the carb needle valve seat!