I own my own ceramic shop and I recently was given more info on mixes of
ceramic slip. I was told that adding barium to the mix makes it whiter.
BUT I also know that barium is poisonous. Does this make it dangerous in
the dry form when cleaning or firing? Any replies would be helpful.

Soluble forms of barium are toxic.
Barium carbonate (Witherite), Barium chloride, Barium Nitrate etc....
are toxic. insoluble barium - ie Barium Sulfate is inert, non-toxic and
can be used for things like barium milkshakes when you get a GI series done.
Barium chloride will poison you.
Once fired into a ceramic - it should be harmless (depending on how well
the Ba is tied up)