MNost common issue with bulbs is they make leak back between while stopped at a fishing spot, have to pump up again.
Often the bulb is replaced and still does it.
Reason, the bulb must be mounted with out let above the inlet.. if not the little ball bearings in the non return valve fall out of the valve stop sealing..
Check easy stuff 1st.
Your issue sounds most likely fuel starvation.
1/ check fuel filters for crap
2/ check ALL fuel lines for any suspect air leaks at joins.
Ideally cut back re fit and re fit the stainless jubilee clips.
This also eliminates the possibility of a flap of fuel hoes interior being peeled off when fitted onto fittings previous time.
3/ check the pick up in the tote( assume tote) is clean clear, no carp in the tote tank.
4/ Check tote tank breather is actually breathing WELL.
5/ Old school vintage/ hot rodding , side of the road carb fix. Run engine, take rpms up to fast idle or little more. put hand over carb inlet, create a good suck vacuum, without stalling the engine, then suddenly remove your hand... repeat 4 to 5 times.
Running an engine, espec engines like outboards chain saws garden blowers etc, that are in the high performance league, lean is serious slow death to the engine...combustion temps get very high
Note: Combustion temp and engine running temps are 2 very different things.