You're right, the float should shut off the fuel from coming in the bowl. That is, of course, if you're not squeezing the bulb so hard that you're over powering the valve.
If you feel that you're not over pressuring the hose, then the float valve has probably developed a leak either from wear or deformation due to ethanol content in the gas you use.
If it's leaking, the float valve should be replaced. If the float valve seat is worn then you may need to replace the carburetor.
The only way to know for sure is to take it off and have a look.
The valve is $13.59 and the carb complete is $98.71 at boats.net
Both appear to be in stock and available depending on what you find.
Good luck.