There are two "models" of the Honda BF8; the "A" model and the "D" model. Since 2001 they have been built concurrently. The "A" model is the updated version of the old blue and white BF100 and has a squarish hood. The "D" model was an all new design (and it shares its block with the BF9.9D) and has a very round hood.
This is important because the "A" model has a traditional choke plate in the carburetor. The "D" model has no choke, even if it has the choke knob you're really pulling a needle valve out of the carb's enrichement circuit; it works exactly the same on the electric start models which do it with electricity (by heating a disc) rather than a cable as on the manual start versions.
To reinterate...the "A" model has a choke; the "D" model has an enrichment circuit. The end result is the same...to get a mixture in the cylinder that will fire but they come at it from totally opposite approaches. The "A" model choke plate retricts the air intake to richen up the charge in the cylinder and the "D" model adds fuel to richen the charge in the cylinder.
Why is this important? Because on the "D" model if you so much as breathe on the throttle handle you'll introduce more air into the fuel mixture and lean it out...it will not start. It must remain in the dead idle position and not be moved until the engine is idling on its own. Resist every temptation to turn that throttle handle; you're just undermining your efforts.
Here's a bit of a tip but please read carefully. BEFORE you ever pull on the starter cord and after you've connected your fuel line and primed the carb you can twist the throttle handle all the way open a couple of times. The "D" model carb does have an accelerator pump and this will give the engine a couple of shots of fuel. Then return the throttle to the dead idle (i.e. - against the stop) position, pull out the "choke" (really enrichment) knob, and start the engine. Feed the knob back in as the engine starts to warm up. NONE of this applies to an "A" model BF8.
Honda engines are frustratingly tight when new. The BF8 through the BF20 are all hard starters until they break in; I think that takes at least 50 hours but at 100 hours they really start to run nicely.
The BF8A model should start on the second pull (or third worst case) every time. If not something is wrong and typically on the "A" model it's the fact the throttle was not opened up AS FAR AS IT WILL GO when trying to start the engine. There is a mechanical stop in the throttle system that limits the opening when the gear lever is in the neutral position. Also the choke (there is a choke plate on this model) must be fully closed...that is, the knob pulled out fully. Do not ease off the choke until the engine is running and is starting to warm up. So the drill is...connect the fuel line, prime the carb, pull the choke knob all the way out, open the throttle as far as possible, pull on the starter cord (a steady long pull is better than a short fast one). The engine should fire on the first or second pull and start on the second or third. On brand new engines it might take an extra pull or two...the darn things are tight!
Let me tell you something about primer bulbs and break a long standing urban myth...they don't need to be pumped until hard. Their only job is to transfer fuel from the tank to the carb bowl. If there's one squirtful more fuel in the carb bowl than needed to start the engine it'll fire. The only think you're doing when you pump the primer bulb until hard is working against the seal the float needle valve makes when the bowl is full...you are not squirting fuel into the engine per se. The only reason to pump until the bulb is firm is to satisfy yourself that you've filled the carb bowl (which isn't really necessary either but it's easier to tell when it's full that when it's "full enough" to start).