What is a private prosecution warrant?

A misdemeanor, not in the police presence, must start with a warrant, as oppose to warrantless stress. That warrant can be signed by cop, witness or both. Sounds like yours is just signed by witness. You will be arrested and will need to bond out. Go ahead and contact a bonding company and if you know the officer handling, let him know you will turn yourself in. Do not discuss the facts of the case, don't even admit to being there or knowing what this is about. Only say "i am going to engine my right to silence and I want a lawyer" but nothing else.

Just to reiterate; it's a class B misdemeanor, punishable by up to 6 months in jail. Assuming for a second that there's even enough evidence to convict you, the jail sentence can be suspended to probation depending on whet your lawyer and the district attorney arrive at as a plea. If you go to trial and are convicted, the judge will determine your sentence, which could be probation, jail time, or a combination of both. As I stated earlier, being convicted of this charge won't put you on the sex offender registry (until, god forbid, your third conviction for it). The best thing you can do is hire a lawyer to investigate your case, challenge the state's likely assumptions about it (possibly with pretrial motions), and make an intelligent decision about whether to contest it at trial or negotiate a plea bargain.

See my other post: hire a good attorney to represent you.