You can add another basic receiver for $5/mo. and have independent channel selection in the bedroom. If you convert composite to RF to use a coax cable it won't be HD so a basic receiver would be the easiest.
I have my box hooked up to my main TV in my bedroom with the HDMI cable. I have the component wires going into a VCR, which I ran to my monitor/TV on my computer desk. Works for me.