Bail, Bail Bonds - As enacted, removes the requirement to place a defendant on a state or federal list or database as a fugitive from justice for failure to appear, unless it's on a felony; authorizes a court to relieve the surety of liability for an undertaking if the defendant has not been placed on the available state or federal list or database within five business days of the entering agency's receipt of the bench warrant or capias. - Amends TCA Title 39 and Title 40. Companion bill has been assigned Public Chapter Number 1026 by the Secretary of State.