Bullhorn bars were originally made from standard "drop" handlebars, with the drops cut off and the bar flipped upside-down. They were intended for special-purpose events, i.e. time trials and record attempts where aerodynamics was considered more important than comfort or multiple hand positions.
My personal opinion is that unless you're in one of those special-purpose events, you're probably better served by a standard drop bar, or, if you prefer a more upright position, a riser, moustache, or "north road" type bar.