I just looked at your manual and the only output your TV has for this is a "fixed" line out L/R audio on the back, no headphone jack. By fixed, it means the level does not change when you change the volume on the TV, it stays at the proper level for the input to an amp.
What you are looking for may exist but you will need 3 things besides your headphones:
1. Wireless Sender for behind TV, hook to Audio L/R Out.
2. Wireless Receiver to get the signal. (Check out www.x10.com) I think they are unloading some pairs for 10 bucks a pop right now.
If you got the X10 or any type of wireless box of the same type, you still need one last part.
3. Inexpensive amp/reciever that has an RCA L/R Audio input (almost all do) and of course a headphone jack.
So your TV will send the audio to the sender, the sender will transmit it wirelessly to its mate, from there it will go from the L/R Out on the wireless audio reciever to the Audio L/R In of your small amp/receiver, where you plug in the headphones as well as control the volume. A cheap one with at least one stereo audio input you can likly find for under 25 bucks somewhere.
Without shipping and tax, and if you snag the 10 buck x10 deal, then you are looking at well under 50 bucks to put this together. It sounds more complex than it really is, just think of it as moving the TV next to the bed, adding an amp, and plugging in, the only difference is no need to move the TV, the wireless units will get the signal to you.
Again, I have not checked prices on wireless headphones but you may be in the same ballpark, but not with your Bose.
This will work, I use one of the X10 sender/receiver rigs to shoot my DVR signal to another room, in my case I needed video also, you just need the audio, and for me it works great.