I have wired a bathroom fan into an exisiting bathroom with two 3-way switches controlling the light above the vanity. One of the existing 3-way switches is in the bedroom beside the bathroom. The power starts at that switch. Black and red 'traveller' wires run to the second 3-way switch inside the bathroom. I replaced the single outlet box in the bathroom with a double box so that I could wire a new 3-way switch for the fan. I ran a red and black wire from the two traveller screws on the existing 3-way switch for the light over to the two traveller screws on the fan switch. I then continued the power from the common screw up to the fan. The problem is that the 3-way switch in the bedroom still controls whether the fan comes on or off. My question is, can I use a single-pole switch for the fan and run the red and black wires from the 3-way switch over to the single switch. THis way, there will always be uninterrupted power to the fan switch. Power should only run through either the black or red wire and not both at the same time.

Thanks.