No bond. That is the standard position on probation violation warrants, and Tarrant County is no exception.
When a judge issues a probation violation warrant, they are responding to a situation where someone was already given an alternative to incarceration and did not comply with the conditions of that agreement. The court's position is that bond was effectively already extended in the form of probation, and a violation of that arrangement removes the presumption that the person will appear voluntarily. Most jurisdictions hold probation violators without bond as a matter of policy until they can appear before the original sentencing judge.
That appearance before the judge is what determines everything. The Tarrant County probation department will be notified that he is in custody, and the court will schedule a hearing. The judge who signed the original probation order and issued the warrant is the person who will ultimately decide the outcome. That judge will review the nature of the violation, his overall record on probation, his history before that, and any mitigating circumstances his attorney presents.
On the question of Fort Worth coming to get him, that depends on where he is currently being held. If he is already in Tarrant County custody, no transport is needed. If he was picked up in another county, Tarrant County will arrange transport to bring him back to face the warrant in their jurisdiction. Either way the process moves toward that hearing before the original judge.
He needs an attorney familiar with Tarrant County probation courts before that hearing. The outcome is largely shaped by what gets presented in that room.