In Mandarin Chinese, the number 8 is prounounced "ba" and the number 1 is pronounced "yi". Put them together and you get "ba-ba-yi" which when spoken fast sounds a bit like "ba-bye" which sounds like the english "bye-bye". Possibily originated from Taiwan, Singapore, or China.

I wonder where these other entries came up with their crap. You all just got schooled.

bye-bye! == bb! == BB! =~ 881

Esoteric internet text equivalent for "BB!" ("byebye!)