The overall plan doesn't sound bad but it presumes the connectors on the front of the TV are outputs. I haven't seen every TV but the ones on the front are usually inputs. Check around back and see if anything is labeled out.

I don't know what you Dish receiver looks like but some have separate audio outputs. Connect that to your Bose and set for aux.

I agree with Mike that the jacks on the front of a TV are (in my experience) generally aux inputs - not outputs. As he said, see if anything is labled "out" or "output".

In addition, littlebug says she/he is plugging the "solo end into the audio outlet" on the Bose. Sounds like you need to find an input (not output) to plug into on the Bose.

Littlebug: The concept is that you're trying to take the signal "out" of the TV and "in" to the Bose radio.

The input jacks on the bose are the two at the top (at the back of the Bose) Like others have said, look for jacks on BACK of TV that say audio out or Out.
Strangely enough some TV's. like the 26 inch Sharp LCD TV
that I use as a "monitor" for this computer, does not have an external audio out, except for a digital one, and that won't work with your Bose.
One hopes after the answers that were given here, that the Op posts the results of connecting the 2 together!!!

Gary