What is the most profitable business on the internet using Bitcoin ?
It all depends on what your talents are, what kind of capital you have available for your business, and what your target demographic is. There are a lot of different and lucrative businesses you can start, but none of them have a good "blanket" that you can drape across the entire demographic pool you have available to you.
One lucrative example, which is now mostly over-saturated, is gambling. High-value and good returns, however so many of them exist now there's no point being involved with that portion of the economy.
So give us something to go off of, what kind of demographic are you targeting?