If the Director continues to makes sure there is no conflict in his scheduling, and he continues to get approval from his superiors for the trips, I see no problem whatsoever.
He is the chief official for the FBI, and the comm and security available on that aircraft would be helpful to him in the event of an emergency.
The only time I would have a problem is if in his use of the jet, it was not available for a mission requiring it. But that allegation has not been made.
Isn’t it true with these expensive jets that they are really only cost-effective if they are used as much as possible?