He has expressed interest in the X-Prize and seems to have an idea that would work. He first discussed the X-Prize with his Proteus design back in 1999. He proposed using the plane to carry a small rocket-propelled crew module up to perhaps 50,000 feet.

An even more radical plane was photographed outside of his Mojave hangar last year and it looks like an even better mothership design. I don't have a link to a picture handy, but it's a very interesting design. Whether or not it's designed for the X-Prize remains to be seen. So far, Burt isn't talking about it. An artist's rendition can be seen here. I'm using an actual photo for my computer wallpaper.

I've heard that the biggest reason why Burt hasn't already done it is that the X-Prize committee hasn't raised all of the money yet.