This is an interesting question.

My travel agent in Hout Bay, not a spring chicken in terms of putting together strange itineraries for me, actually told me that she really couldn't put together anything for Burundi for me (granted I'm more of a 5-star hotel person), as when she looked there just wasn't an infrastructure for tourism there. This was about 2-3 years ago.

That said, though, you cannot be the first person who wants to visit Burundi, and I'm hoping that you (and I, by extension) get some input on this, as I'd love to visit Burundi myself...