This design allows for dispensing a single tea bag multiple times. It consists of a continuous rotation servo that revolves a slotted circle. There is a slot for each tea bag (this design can hold up to 9 bags).

There is a gap the size of the one slot which allows a tea bag to fall through the slot as the servo moves. 

There is a light sensor and an LED by the slot where the tea bag falls through. When a tea bag falls through it will break the beam and indicate that a tea bag has been dispensed.