Bam Margera -- I Spent a Night in Jail FOR NOTHING

Bam Margera still has no idea why he was arrested Monday in New Orleans -- telling TMZ Live, he was hauled to jail ... spent the night behind bars ... but was NEVER booked for a crime.

TMZ broke the story ... Bam was cuffed in the French Quarter after a Mardi Gras party -- when he jumped in to a pool, fully clothed.

But Bam insists, he didn't break the law -- and when he asked why he was brought in to the station in handcuffs, the cops couldn't give him an answer.

When he was released the next morning, Bam says he never received a ticket OR an explanation -- nothing. He's still stumped.