This really depends on the judge. Some judges won't even consider recalling a warrant and will require you to turn yourself into the jail. Others will allow your attorney to set the motion within a day or two. And still others will set the hearing, but might make you wait several weeks for a court date.
The best person to answer your question is the attorney you retained to handle the process for you. how long it takes may depend on many factors including your attorney's time availability.
Probably not the answer you are looking for but it depends on the judge. An attorney has a few options including a motion to recall or withdraw the warrant, setting the case for a turn in date with the understanding that the case will be resolved prior to being taken into custody or a plea and waiver/ plea in abstentia for misdemeanor cases. Some judges want the case resolved others want some flesh for not appearing. Your history also can be a factor. Contact a local attorney and they will get it resolved by the best available method. You need to hire an attorney because the public defender is not available prior to incarceration.