In cases of felony, when the accused is in custody of the sheriff or other officer, and the court before which the prosecution is pending is in session in the county where the accused is in custody, the court shall fix the amount of bail, if it is a bailable case and determine if the accused is eligible for a personal bond; and the sheriff or other peace officer, unless it be the police of a city, or a jailer licensed under Chapter 1701, Occupations Code, is authorized to take a bail bond of the accused in the amount as fixed by the court, to be approved by such officer taking the same, and will thereupon discharge the accused from custody. The defendant and the defendant’s sureties are not required to appear in court.