The character controller doesn’t really support bullet yet, it’s still very much a work in progress. If you or anyone else is willing to help implement it, it’d be appreciated indeed but until then I can’t really give you an estimation of when the bullet version will be ready and up the same level as the internal physics version.
I also haven’t looked into the bullet code of the char controller in a while, so I’m not sure where I left it, but the registerRayCheck should be a comparatively simple function which you can compare to the one in the “internal” version, it shouldn’t actually differ that much.