The basic principle from Handbook 2 is that an elder should not stand in the circle when a high priest is ordained or when a man is set apart to an office that requires him to be a high priest. A bishop must be a high priest, so only those who hold that office should stand in the circle when a bishop is set apart.
The question then becomes if a person must also be an ordained bishop. Since the priesthood office of bishop is an Aaronic Priesthood office, and since the Melchizedek Priesthood presides over the Aaronic Priesthood, I believe the answer is no. Of course, the First Presidency determines who is to be ordained to the office of a bishop in the Aaronic Priesthood, and gives the stake president permission to ordain a new bishop if needed before he is set apart.
But a stake president does not have to hold the Aaronic Priesthood office of bishop to ordain a bishop. He does it by his authority as a high priest (and with First Presidency permission). So if the stake president does not need to be an ordained bishop (and many times is not), I see no reason that others in the circle would need to hold that Aaronic Priesthood office either.
All that said, even though a high priest, the stake president did not allow me or his father to stand in the circle when my son-in-law was ordained and set apart as bishop. His father first ordained him a high priest, and I stood in that circle, but we then only witnessed his ordination and setting apart as bishop. The stake president and his counselors were the only ones who stood in the circle.
On the other hand, I always allowed a worthy father who was a high priest to stand in the circle when his son was ordained and set apart as bishop. If the son needed to be ordained a high priest, I normally let the father ordain him first, and then we continued on as I ordained and then set him apart as bishop, which only I was authorized by the First Presidency to do.