The primer bulb isnt the source of your fuel leak, the needle and seat within the carburettor will be passing fuel and flooding it out the primer line. personally to start with id remove and clean the carb cap (On the back of the carb from the perspective of your photo, replace the rubber o ring and clean the float area (be careful and dont lose the needle) i have had issues with white primer caps over the years but never had an issue with these old remote primer carbs other than a little dirt buildup or the fuel tap being left on and forgotten about.
