I'd say "shoot" is coyer/cutesy. "Bull" is quite harsh.
It's also unlikely to be from "bullshit", although people do use it that way:
"insincere, trifling, or deceptive talk," 1914. Popularly associated with roughly contemporary bullshit (n.) in the same sense, and in modern use often felt as a shortened form of it. There seems to have been an identical Middle English word meaning "false talk, fraud," apparently from Old French bole "deception, trick, scheming, intrigue," and perhaps related to modern Icelandic bull "nonsense."
also bull shit, "eloquent and insincere rhetoric," 1914, American English slang; see bull (n.1) + shit (n.), probably because it smells. But bull in the sense of "trivial or false statements" (1914), which usually is associated with this, might be a continuation of Middle English bull "false talk, fraud" (see bull (n.3)).