In Bossier Parish, Louisana, to press charges for simple battery, how long do you have to contact the police/ file a report from when the incident happened?

I don't think there is a limit anywhere, but the prosecutor's office will assess the charge as a whole and decide if they want to follow through. As anywhere, the longer you wait, the more evidence is lost and the more your credibility is decreased. If someone hurt you and you didn't realize that you needed medical attention, or you didn't realize that the pain would continue, you might be able to go on testimony of others. But nothing is etched in stone.
You can also file civil charges (monetary damages) on your own, in Small Claims, such as for medical bills.

There is a statue of limitation on a crime, for a midemeanor I forget either 6 months or one year.

But the longer you wait, after a few hours or a day at the most, the less likely the DA and police will do anything.