Wireless Speaker Can I buy a Hi Fi system that will connect wirelessly to a separate speaker in my bedroom?

Yes Yamaha makes a couple of stereo receivers that have music cast wireless out capability... Some Denon AV Receivers use Heos which is a wireless connection method that can be used to transmit a wireless music signal through out the house to other Heos speaker or other Play Fi speakers. There is also Sonos which can use a transmitter connected to your receiver for sound..Trouble with Sonos is that it will only work with other Sonos equipment...I think Onkyo also has some kind of Play Fi compatible system mostly available in its AV receivers but also available in some of its network stereo receivers....

There are ways to do it, but I wouldn't.

Wires cannot be beat for their low cost and nearly perfect reliability.

If you Simply Must do it, get a Bluetooth transmitter.

Be careful --- there are also Bluetooth receivers,

which won't do what you want in this case.