Hmm...this seems like a trick question, so I'll try to be as thorough as possible. There is a 2nd quest after you beat the game (Goombas are replaced with Buzzy Beetles, etc.), and a 3rd quest, and a 4th...on and on...if you look at it that way, there are an infinite number of Bowsers. If you look at anything past the 2nd quest as being redundant, then there are 16 Bowsers. However, there are a total of eight Bowsers throughout the first quest, as you only see him in the 4th level of every world.
But I'm not sure what answer you are looking for...so none of these is my "official" answer (in other words, I don't want to lose any points
)