You need some sort of "Video Sender", which will take the signal from the living room's Sky box & send it to the TV in the bedroom.
e.g.
http://www.maplin.co.uk/Family.aspx?...605&worldid=-9
http://www.argos.co.uk/static/Produc...IDEOSENDER.htm
http://www.argos.co.uk/static/Produc...IDEOSENDER.htm
You will only be able to watch the channel currently selected by the living room's Sky box, but some video senders can also relay the remote control signals, so you can use your remote in the bedroom.