The starter cannot randomly engage. It engages with the energizing of the solenoid which spins the bendix drive forward to engage the flywheel. The bendix also
contains a overrun clutch which would allow the engine to turn faster than the starter. So if your bendix was sticking, it wouldn't slow your engine and make the car buck.
If your starter was trying to randomly engage, you would hear the starter gear grinding against the spinning flywheel.
Ever hear someone engage the starter on a running engine? That's what you'd hear.
Now when you say the starter died, maybe you have an electrical problem that has finally shown itself in a big way.