In Texas you have a right to bail under the State Constitution. However, in recent years the Texas Constitution has been amended to allow no bonds to be set in certain cases. Texas has a Bill of Rights, and the Bail provision are under section 11 of Article 1. If you are trying to bond lowered, or have an issue with bail, the Constitution of Texas is something you should look at.
Sec. 11. BAIL. All prisoners shall be bailable by sufficient sureties, unless for capital offenses, when the proof is evident; but this provision shall not be so construed as to prevent bail after indictment found upon examination of the evidence, in such manner as may be prescribed by law
Sec. 11a. DENIAL OF BAIL AFTER MULTIPLE FELONIES. (a) Any person (1) accused of a felony less than capital in this State, who has been theretofore twice convicted of a felony, the second conviction being subsequent to the first, both in point of time of commission of the offense and conviction therefor, (2) accused of a felony less than capital in this State, committed while on bail for a prior felony for which he has been indicted, (3) accused of a felony less than capital in this State involving the use of a deadly weapon after being convicted of a prior felony, or (4) accused of a violent or sexual offense committed while under the supervision of a criminal justice agency of the State or a political subdivision of the State for a prior felony, after a hearing, and upon evidence substantially showing the guilt of the accused of the offense in (1) or (3) above, of the offense committed while on bail in (2) above, or of the offense in (4) above committed while under the supervision of a criminal justice agency of the State or a political subdivision of the State for a prior felony, may be denied bail pending trial, by a district judge in this State, if said order denying bail pending trial is issued within seven calendar days subsequent to the time of incarceration of the accused; provided, however, that if the accused is not accorded a trial upon the accusation under (1) or (3) above, the accusation and indictment used under (2) above, or the accusation or indictment used under (4) above within sixty (60) days from the time of his incarceration upon the accusation, the order denying bail shall be automatically set aside, unless a continuance is obtained upon the motion or request of the accused; provided, further, that the right of appeal to the Court of Criminal Appeals of this State is expressly accorded the accused for a review of any judgment or order made hereunder, and said appeal shall be given preference by the Court of Criminal Appeals.