Bishop's departure comes as part of a restructuring programme both on and off the pitch at the Recreation Ground.
The 39-year-old arrived alongside boss Dean Holdsworth in January 2011 after the pair worked together at non-league Newport.
Holdsworth said: "Bish and I have been through so much together and shared some excellent times. It has been enjoyable working with him and his work-ethic is fantastic.
"The management and players wish him all the best and thank him for the contribution he has made. He has been part of a special relationship. We wish him every success for the future."
Holdsworth and as his coaching staff, including Bishop, signed new one-year contract extensions last summer to keep them at Aldershot until 2014.
Shots currently find themselves two points and two places above the drop zone in League Two.