I think it would be helpful if she still had a cage in your room, even if the door is always open. It really helps rabbits to feel secure if they have a space that is their own, with all their stuff in it. A whole room can be quite overwhelming for a shy bunny at first.
If you sit on the floor, eventually she’ll come out to investigate. She’s probably just a bit disoriented by the move. You could also try scattering treats over the floor to see if that would entice her out, but it’s still quite recent since the move, so it could just be that. Also what’s your flooring like? Some bunnies struggle with slippery flooring, so putting rugs down if it’s tiles or shiny wood might help.
As for litter, it really helps to litter train them if there’s a separate substance in the litter tray. I use paper based pellets (back2nature, which I think are Yesterdays News in the US) that are great, and lots of people use non-clumping pine pellets too.