If I went there on a Thursday night just for the bar, how likely is it that I would be able to snag the burger? Is it not a secret menu item any more and always available?

It's a $31 burger. They will always have enough for everyone. Lol.

Just in general, it's hard to get a seat at the bar. I recommend securing a reservation for a table in the bar area.

I have never had a problem getting the burger for lunch, but never tried for dinner.