Legal Question in Criminal Law in California

Slander, libel, and defamation are not distinct causes of action. Slander and libel are just specific types of defamation. Defamation involves false statements to third parties, but an arrest isn't a statement. That means it can't be defamatory. Statements made in the course of the arrest, booking, etc. could be defamatory in principle, but public officials are immune for any such statements they make in the course and scope of their duties.

You have the option of suing for false arrest, but you could only win such a lawsuit if you can prove both that you are innocent of the charges and that the police had no reason to believe you were guilty. Police often make good-faith mistakes, and they are not liable when that happens. You also don't have a claim against anyone who may have accused you to the police, since police reports are privileged from defamation lawsuits.

I'm afraid you have to pay the bail bondsman, too. He's a private businessman, who made a deal with you and kept his end of the bargain. You have to keep yours. The fact that the D.A. decided not to pursue the case doesn't excuse you from paying your bill. That's true even if you're innocent and can prove it.

Sorry I can't be more encouraging.