I was wondering if I get a B.A. in business can I get a B.A. at a culinary school??

Are you asking if the school will let you do it or you are asking if we know you have the capability to do this?
If you mean if the school allows it...
Based on my experience, YES, you sure can!
I had a BS in ACCT and a BS in Engineering with a BS minor in MATHS.

Why not? My sister has 2 BAs and a Master's.