capacitor70, I am not very skilled in electronics, but I have a few thougts about your schematic.
First of all, let's analise how your capacitor charges.
At 60Hz, after the bridge rectifier you will have 120Hz impulses. At this frequency, your 330uF capacitor has a internal resistance of 1/2 x pi x f x C= 4 Ohm.
Using a bulb, the resistance increases. I have measured a 100W/230V bulb, and it has 30 Ohms.
Let's say yours has 15 Ohms. This is added to the 4 Ohms of the capacitor, resulting 19 Ohm.
The time constant (T) now is R x C= 0.00627s, or 6.27ms.
The capacitor will charge at 98% of your 230V source in 4T=0.025s, or 25ms. That's a lot of time!
At 2500rpm, the engine makes 1 full turn in 24ms. Doubling the rpm, the time for 1 full turn is half than that. If it is one cylinder 4stroke engine, that means the spark fires every 2 turns.
Please measure the resistance of the bulb.
If your bulb has a bigger internal resistance, the results will be worse than that... And we need to add the on-resistance of the bridge too, although is not too big.

In your setup, if ihe capacitor is charged by the electric generator in your engine (bike), then probably it will not run at 60Hz when you try to start it. It probably needs to idle at 800 or 1000 rpm to do this. I am not shure of that, but you need to think about every thing...
The conclusion is that the bulb may protect the inverter, but it works against the capacitor.
The frequency is too low for the capacitor needs.
It would be better to find a way to stop the inverter for that period of time when the capacitor discharges, and to pull the bulb out of the schematic, allowing the capacitor to recharge faster.
These are my thoughts. Hope it will help somehow...
Good luck and don't stop!

I had a problem with the internet conection, and the post apeared twice...
Sorry...

Hello all!
Although it may be too soon to try...
Why don't drive part of exhaust gas directly into carburetor?
Just a more or less long tube to allow it to cool a little, exaust gas mut be mostly water perfectly conditioned to restart to blow.

I know it sound silly but maybe this is is the try-everything-time.
If anyone can try I will report as soon as I can complete test, may delay a little due to lack of time.

Please excuse if any unconvenience, my English and keyboard have their own ideas.
Cheers
Ri

Bulbs are for just experiment purpose, Previously I am using 700Hz 230V 100Watt Inverter, wattage is problem.

Inverter is in my mind, I am having 200Amps 1200V IGBT pairs for inverter, but right now more focus on starting engine in ideal to get all needed conditions.

major problem is right now is spark plug gets shorted with water and engine oil on its tip, many times it requires opening and cleaning again and again. On my table setup I checked different size spark plugs, 0.5", 0.75" and
1" diameter, I got best results with bigger spark plug. It gives both advantages prevent shorting and more area for
water burning. flame size is without water 0.5" and with water 1.5 to 2 inch in diameter. you can see these photos on previous posts it is with only 175V DC

For those of you suggesting doing this on a 2-stroke motor... It will ruin the motor very quickly.

In a 2-stroke engine  the oil and gas mixture is pulled from the carburetor and then circulated through the engine crankcase before finally ending up in the combustion chamber.
This works the same in both oil injected and premixed engines. If you substitute water for the gas you will be lubricating your engine with an oil/water mix and the engine bearings will develop rust pits within days.