Did Bruce Wayne inherit Wayne Manor?

Most likely if Alfred is still alive he would get a portion and the rest would probably go to various charitable organizations.

I think Alfred would likely get some, and Dick Grayson, Tim Drake, Stephanie Brown and Carrie Kelly would probably get some as well, since they are the only 4 living people who have held the Robin title. The other 2 Robin's Jason Todd and Bruce's son, Damien have died in the main continuity.