First off, I have been playing Bari exclusively for almost 30 years and I had trouble getting below a low F on a Jean Baptiste bari. They are not good.
If you can find another bari, try that.
Any stock mouthpiece will give you an idea on where to go for a mouthpiece. Also, try matching your set up on tenor. If you are playing a tenor piece such as a Link 5star, try a Link 5star on bari, for example. This will not be perfect, but will get you closer than just randomly picking a mouthpiece.
From your brief description of your problem here, I would guess your problem is about 90% horn and 10% you and your reed/moutpiece set up.
I have never had a tenor sax student not play below a low F on my bari. A low B maybe, but not a low F. Alto students are another story.
Good luck. Let us know what you do.