To express one’s opinions on a variety of matters, whether or not one knows a great deal about them. Bull here appears to be a shortening of bullshit, which has meant nonsense, lies, or exaggeration since the early 1900s. A gathering for shooting the bull is called a bull session and traditionally consists entirely of males. Yet another euphemism for shooting the bull is shooting the breeze, which calls up the image of the hot air expended in this kind of a gossip session. To shoot one’s mouth off, on the other hand, means both to talk indiscreetly or tactlessly and to exaggerate.