Light switch won't turn on unless switch in adjacent room turned on
Most likely the bedroom light is wired downstream from the bathroom light, but the wiring in the bathroom switch box is wrong. To investigate further, turn off the circuit, remove the switch wallplates, unscrew the switch from the box, and take a good look at the wiring. Post a picture here for more specific help.

Most likely problem: the bathroom switch box has some mixed up wiring that can be fixed by connecting the wires that are already there in a different way. This would apply if that switch box has three cables (each a 3-wire bundle: black, white, ground) coming into it. One is the power supply, one goes to the bath light, and one continues to the bedroom. If that's the case then your problem is that the bedroom is wired to the switched power instead of to the constant supply power.