From what I quoted ... BBM
JPATS supports the federal judiciary through its scheduling and transportation responsibilities. JPATS transports sentenced prisoners who are in the custody of the Federal Bureau of Prisons (BOP) as well as to hearings, court appearances and detention facilities. Military and civilian law enforcement agencies use JPATS to shuttle their prisoners between different jurisdictions at a fraction of what commercial sources would charge.
I was actually thinking that they might put her on a AMC (Air Mobility Command) flight. AMC is kind of like a military airline. It also operates Air Force One and lots of smaller private VIP aircraft. There is a unit at Joint Base Pearl Harbor Hickam. Wouldn't surprise me at all to hear that they actually operate the JPATS flights. Hard to believe there would otherwise be enough demand to move federal prisoners between the mainland and Hawaii. It would be cheaper to put her on a USAF Learjet.
Also note that Hawaii houses a lot of its prison population in Arizona and elsewhere on the mainland so there must be some regular system in place to transport them even if is not JPATS