2001 Pontiac Bonneville RPMs surging up and down at normal

With that many miles on it there are a lot of possibilities. My first suspicion would be that the throttle body could be worn out and leaking vacuum pretty badly. You could also have an EGR valve stuck open but that should put the check engine light on. That particular engine also has a lot of problems with the plastic intake manifold deteriorating and leaking from the bottom.
A sharp tech could hook up a scan tool and analyze the sensor data and possibly come up with a conclusion.