So reporting back after the winter, I replaced the primer bulb (actually the whole Air Filter & Primer Base) and it still won't start. The chances of getting a bad one seems low but I'm not sure what else it could be. It is hard to tell if fuel is making it in as it is hard to see.
Reminder, mower wouldn't start towards the end of the last season. Spraying some carb cleaner in the cylinder caused it to start to the assumption was that the primer bulb was bad. Didn't really have a chance to test it til recently.