Is getting arrested on bench warrant the same as turning yourself in?

Handing yourself in voluntarily will at least show the court you are taking things seriously. Waiting until you get hauled in by law enforcement will give them a less favourable impression of you.

Once you are in custody, what happens next will depend on how they see you. If they see you as seriously wanting to get things concluded, you may be released on bail until the new hearing. If they see you as a flight risk or suspect you'll avoid the new hearing, they may keep you in custody to ensure you're there.