But the OP is not being prosecuted by the state. He is facing federal prosecution, and the term "personal recognizance" is very much used. It's in the applicable statute, 18 USC § 3142(b):
(b) Release on Personal Recognizance or Unsecured Appearance Bond.-The judicial officer shall order the pretrial release of the person on personal recognizance, or upon execution of an unsecured appearance bond in an amount specified by the court, subject to the condition that the person not commit a Federal, State, or local crime during the period of release and subject to the condition that the person cooperate in the collection of a DNA sample from the person if the collection of such a sample is authorized pursuant to section 3 of the DNA Analysis Backlog Elimination Act of 2000 (42 U.S.C. 14135a),1 unless the judicial officer determines that such release will not reasonably assure the appearance of the person as required or will endanger the safety of any other person or the community.