How can I make a basement bedroom look brighter?

Light paint colors reflect light back into the room, making it appear bigger.  You could also try light-colored accessories and decorations, as they will also help. Try to place as many lights in the room as possible and connect them so they all turn on with the flip of a switch—by dividing the light source, there seems to be more even light throughout the room as opposed to relying on a single source.