In NJ the defendant can ask once every xxx amount of days. The longer the imprisonment in the local jail the more the bail might be reduced. Unless it's a capital crime then no chance of much reduction at all.

http://criminal-law.freeadvice.com/criminal-law/criminal-law/bond-reduction.htm

Texas specific from this piece:

Bond Reduction Requirements
Inability to pay is only one element of a bond reduction motion and hearing. It is a significant factor, but many jurisdictions require a defendant to jump through additional hoops. For example, in Texas, a defendant is required to show that he has actually made an effort to post the current bond before the court can even consider a bond reduction. This threshold requirement can be met by testimony from a friend or relative regarding the number of bondsmen they have called in an attempt to make the current bond.

If a defendant is seeking a bond reduction because there has been a delay in indictment, then he should present some evidence regarding how long he has already been in custody without being formally charged. Texas will require a court to lower bail when a defendant has been held 90 days or more in jail without the return of an indictment. In exchange for a bond reduction, a defendant may offer to be subject to conditions, like electronic monitoring, to help the court feel more comfortable in reducing the bond and thereby enabling release from jail.

Here was an interesting part:

Consequences of Seeking a Bond Reduction
Every defendant wants a cheaper bond, especially in times of economic instability. Some defendants push their attorneys to file a bond reduction on the theory that the worst case scenario is the judge denying the reduction. A defendant should understand how the jurisdiction functions before filing a bond reduction. A judge may grant the motion and the defendant can move on peacefully. However, once a defendant files the bond reduction motion, the State may decide to file a motion to increase bond or add strict bond conditions.

Bond hearings often result in a defendant disclosing evidence to the state. Sometimes this disclosure can hurt a defendant on the prosecution side. At the very least, a defendant may have drawn unwanted attention. Once a prosecutor becomes more involved with a case, the more targeted a defendant’s case can become. For all of the perceived advantages, a bond reduction motion has its share of potential disadvantages.

Because of this, I would highly recommend consulting with an attorney before you try to do it on your own. A lot of times consults can be free.

-independent

Here are the Texas statutes about bail as well.

http://www.statutes.legis.state.tx.us/Docs/CR/htm/CR.17.htm

That is a lot to dig through, the first article does a pretty decent job of summarizing the statutes, but you may want to re-read the statutes.

Definitely go talk to a criminal defense lawyer for a free consult.

thank you!