According to Forbes
the first content DLC is action-based and released today. Burial at Sea is to come out later.
Big news out of still-possible-GOTY-contender BioShock Infinite today, as Ken Levine announced two separate pieces of downloadable content for the game. The first is out today, and called Clash in the Clouds. It’s a difficult, battle arena-style event modeled after the games tough 1999 mode. Players will complete challenges by killing enemies under certain conditions, and use the cash they win to unlock bonuses like audio files or concept art.
If today's DLC is part of the Season Pass, I'm glad I didn't buy it because it sounds pretty uninteresting to me. I'll be interested in BaS though.