The most common type of warrant is a warrant that is issued by the Court when you fail to appear in Court on the date you were scheduled to appear. It typically referred to as a bench warrant. The failure to appear refers to the defendant’s failure to appear not the attorney’s failure to appear. While it is true your attorney is required appear on your behalf once retained, it is not a valid reason to place bail on a defendant. In the State of New York Criminal Procedure Law 510.30 set forth the factors a court should consider when setting bail on a defendant, they include: The defendant’s character, reputation, habits and mental condition; His employment and financial resources; His family ties and the length of his residence if any in the community; and His criminal record if any; His previous record if any in responding to court appearances when required or with respect to flight to avoid criminal prosecution; and If he is a defendant, the weight of the evidence against him in the pending criminal action and any other factor indicating probability or improbability of conviction. Your attorney's failure to appear is not a factor a court is to consider when placing bail on a defendant.
Bail is not a function of whether your lawyer is present. It's supposed to be decided by the judge on the basis of whether you are considered a risk to not appear at your trial and on the seriousness of the crime.
Setting bail is at the discretion of the judge at arraignment. It can be appealed, but such appeals are both time consuming and almost always fruitless.