Short for "Break Up, Make Up, Sex You Up." Or the act of breaking up, making up, and subsequently sexing up with one's on again/off again girlfriend/boyfriend.
Appears to have originated in Hawaii high schools in around 2007. Being particularly fond of the word "Bu" (short for "bull", used in casual greetings normally between males), "bumusu" has grown to connote having high sexual prowess with girls. So much so, that you frequently go out with, break up, make up, and sex numerous girls simultaneously and/or consecutively in a calculated manner.
"What's up with you and your girl bro?"
"Eh. You know. Bumusu."
"Hooo bull. How many chicks is that this month? Fuckin bumusu, man."