I think you’re confused because you would never use “shit”/“shat” transitively. you shit *at* people, you don’t shit them (I sincerely hope). a more obviously transitive verb might be “punch” as opposed to “talk”. so you “talk to me” or “talked to me” but you “punch me” or “punched me”. bullshit is like punch: you bullshit people, you don’t bullshit at them, so if it happened in the past, you punched them or bullshat them.

the final confusing quirk is that in my subtitle the past participle is being used as an adjective, but that doesn’t change the conjugation.