Your starter drive/clutch is slipping and needs to be replaced. Inside the drive is a cam and roller setup that locks when it turns in one direction, and releases in the the other direction. If the rollers or cam get worn or the springs break, the clutch won't engage properly and the starter acts as you describe.
That drive type is an over-running clutch that prevents the starter armature from over-speeding when the engine starts, because the drive gear remains engaged with the flywheel until you release the starter pedal, or solenoid switch if you have a solenoid starter.
A Bendix drive is a different drive that uses acceleration of the starter armature to drive the gear along a spiral spline on the armature shaft and into the flywheel. Sometimes the gear engaged with pretty hard clash. Bendix drives use a spring to disengage the starter drive gear when you release the starter switch, but the Bendix drive also disengages the drive gear by 'unwinding' the drive gear, so to speak, along the spiral spline on the armature shaft when the engine starts. The Bendix drive would also disengage if one cylinder fired, but the engine didn't start and run, so starting a balky engine could be a frustrating experience- you had to let the starter motor stop almost completely before the Bendix drive would engage again. They were also called an 'inertia drive' because they used the armature acceleration to drive the starter gear into the flywheel.
Bendix drive starters haven't been used for several decades, but were common on vehicles prior to about the mid-1950s, although I don't think Chevrolet ever used them. Delco-Remy did make some Bendix-drive starters, I believe, but I don't know if any GM vehicle used them. Bendix-drive starters were mostly made by Electric Autolite and Ford, maybe some others.
As a bit shop-talk history, replacing the 'Bendix' was the common reference when replacing any starter drive, regardless of the starter being a Bendix-drive or an over-running clutch type-- in case anyone is interested in that tidbit.
Harvester