I have a 220 volt breaker feeding a 2 circuit panel in a detached garage (50 ft away). It is fed from an outside panel beside the service entrance where the air conditioner used to be. The double pole breaker red and black. Neutral and ground go to the main neutral/ground bus bar.(Ground rod and entrance neutral). In the garage, red 20 amp breaker black 15 amp breaker white goes to the neutral bus bar... bare goes to a separate grounding bar. If this is up to par, do I need to add a ground rod at the garage.

Yes, a panel in a separate structure needs at least one ground rod, connected to the equipment ground bar with a mimimum of #6 copper wire.

Check local codes, some states require two ground rods or other grounding electrodes.