There is no limitation. However you can file bail application a second time only after you have some new facts coming to light or if circumstances materially alter. Else it will be just thrown out. But you can go to higher court immediately after your bail is rejected in the lower court.
Those conditions normally involve refraining from using or possessing alcohol, firearms, and drugs (unless prescribed by a physician) while out on bond, not violating any other laws while out on bond, and in cases of violence, having no contact with the victim in the case.
If the defendant cannot post bail, they will remain in custody, but they can also ask family or friends to help them. Alternatively, they may be able to engage a bail bond company to post the bail on their behalf. The court denies bail and the defendant remains in custody until their court hearing.
And while some will tell you that you can't remain anonymous, the short answer is actually yes, you can. (But with one major consideration.) The Court is going to need a name and person to return the bond to once the court date has been successfully completed.
The court can grant bail after considering various factors, such as the nature of the offence, the evidence against the accused person, the likelihood of the accused person absconding, and the possibility of the accused person tampering with evidence or influencing witnesses.