What meaning of/phrase based on the verb to call is used in "I call [noun]" (for instance bull****) and considerations with count nouns?

To call in that usage means to announce a judgment on a particular action or circumstance, as one who is formally or informally recognized as having the authority to render such judgments in the domain in question.

I call foul!

The referee called the play dead.

The first example might be heard in an informal "pickup" (i.e. impromptu) game with no referee, where the player is recognized as having the "authority" to say that he has been fouled by another player.

The second example refers to a person, the referee, who is empowered to make such judgments.

The phrase can be used in circumstances not involving a game, treating those circumstances as if game rules applied to them, or at least wishing they did.

Perhaps something shouted by Mikey's younger brother whom Mikey is tormenting:

Mom! Mikey's says he is going to eat the last cookie which I was saving for my lunch tomorrow. I call foul!

In phrases like "I call bullshit" the speaker is being facetious and acting as if he is in the role of referee, and a violation of the Bullshit Rule has occurred.