I have an older mower that runs OK. However, lately after about 10 min of running, it starts to choke out. When this happens, the primer bulb is sucked back into the mower. I can wait a few minutes or just manually pull the bulb back out and will run a few more minutes. What would cause the bulb to suck in like that while the mower is running?

A bad vent cap on the fuel tank can cause this.

Mowerman nailed it and to prove it is your problem run the engine with the cap slightly ajar. Bet the bulb stys in place.