Hi and welcome to FixYa, I am Kelly.
The symptoms you describe are typical of debris in the fuel bowl of the carb. I am going to assume for the moment that it is a similar to a Briggs and Stratton engine. Engine model type and serial information is what we work with to resolve engine problems regardless of the mower brand. I note you said it was a Scott Bonner SX4000 engine. I am also assuming that you have the 18 inch GreenKeeper like this one:
I do not have access to Scott Bonner Engine parts or technical data but if you clean out the fuel float bowl
and it is still hard to start then the choke function of the engine is not working. Your engine has a "Bowl drain" screw on the bottom of the carb float bowl for removing carb debris or water in addition to a bowl nut.
Most likely due to the throttle cable needing and adjustment so that the choke is closed when choke is selected. Adjustment of the throttle cable is as simple as losening the clamp screw (Do NOT remove it) on the side of the carb throttle control and moving the throttle to STOP then re-tightening the clamp retaining screw. This should allow your choke to move full closed when selected. You may have to experiment with full throttle and STOP throttle control positions with the clamp screw loose but not removed to see which position will give you full throttle, choke and STOP. After each adjustment you MUST tighten the clamp screw to test the throttle cable travel on the the throttle plate. Beleive it or not... the person that assemble the mower made the intial throttle adjustment. It may have never been tested before you got the mower.
If you still have problems.... this is the brief way to start an engine that has choke problems. Remove the spark plug and squirt a splash of gas into the spark plug hole and then re-install the spark plug. Just don't over-do the splash of gas and if your messy wipe off the excess so you do not start a fire. (This method always works but you occasionally foul a spark plug with too much gas)
Thanks for choosing FixYa,