The "bull" in "bullshit" is unrelated the "bull" meaning "a ludicrous jest." It is, as suggested, a portmanteau of "bull" (n.1 in the OED) "the male of any bovine animal", and "shit." 

 According to the OED, the "ludicrous jest" version (n.4) is is not derived from Papal Bull: 

 "No foundation appears for the guess that the word originated in ‘a contemptuous allusion to papal edicts’, nor for the assertion of the ‘British Apollo’ (No. 22. 1708) that ‘it became a Proverb from the repeated Blunders of one Obadiah Bull, a Lawyer of London, who liv'd in the Reign of K. Henry the Seventh’." 

 I'm sorry, but I don't know how to cite the OED, as I have the electronic version.    

  

 Oh wait, I take that back. This is how they have in the OED: 

 [f. bull n.1 + shit n.]  

 1.1 Rubbish, nonsense; = bull n.4 3. 

 First they have it in the n.1 sense, then in the n.4 sense just below, so I'm not sure.