Re: advise needed
Not meaning to put you down in any way, but your question isn't clear. Are you saying your tank has a dual hose? That would be in the 1950's. And it shouldn't have a "bulb", but a primer button on the tank. Pumping the primer button fills the carburetor so you can start the motor. Once running, the motor pumps air into the tank, presurizing it. Pressure in the tank pushes fuel to the motor so it stays running. If it does not pressurize the tank, you have an air leak somewhere. Just fix it already.
However if you actually do have a 1960's motor with a primer bulb, you then have a single hose fuel tank system with a fuel pump on the motor. If it won't stay running, the fuel pump is shot, or again you have a leak somewhere. The cure is the same, fix the problem.
If you are asking if it is possible to convert the pressure tank system to a single hose, the answer is yes. We can argue all day on the merits of that.