Not to get you down or anything, but I think it may be about time to retire the old Bose system. I looked up the manual for it on Bose's website and happened to notice this particular model was produced between 1998 and 2000. The thing's going on nearly 20 years old. I even saw a reference to laserdisc in the manual. Best case scenario, you're going to get stereo from your Apple TV and not surround sound. Looks to me like your only option is to use a stereo RCA cable and connect the TV's variable audio out to one of the Bose's audio inputs.

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This is assuming of course, that the 'variable audio out' does what I think it does. Not to get you down or anything, but I think it may be about time to retire the old Bose system. I looked up the manual for it on Bose's website and happened to notice this particular model was produced between 1998 and 2000. The thing's going on nearly 20 years old. I even saw a reference to laserdisc in the manual. Best case scenario, you're going to get stereo from your Apple TV and not surround sound.

Looks to me like your only option is to use a stereo RCA cable and connect the TV's variable audio out to one of the Bose's audio inputs. This is assuming of course, that the 'variable audio out' does what I think it does. OP, again, note the issue with your connection option here. You can't push stereo sound from the TV and have it yield 5.1 surround sound audio as 5.1 is intended. The jacks diagram for the Bose is too small to be certain about what connection for real 5.1 is there: is there at least an optical audio jack IN(put) on that unit? If not, the Bose appears to be creating faux surround by taking stereo audio in and 'faking it' by pushing that to the 5 speakers attached.

This can work OK but it is not real 5.1 surround (because you are asking technology to guess what sounds should come out of each speaker instead of letting- say- a movie or TV soundtrack send the actual sound intended for each speaker to the correct speaker). Maybe you don't care about that but it would make a big difference in all audio for almost all movies & TV shows you might watch via TV if you could push real 5.1 to your speakers. If the Bose unit does have some way to get 5.1 into it (so it CAN push 5.1 to the speakers), that is the connection that must be made here (which appears to cut trying to wire through your TV out, because IT doesn't have any digital audio out options like an HDMI or optical audio out jack). A Left & right (red & white cable) stereo connection will NOT accomplish pushing surround sound out of the TV and into the Bose; it will be stereo audio only going into the Bose. How you get real surround out of TV and into something connected to 5 speakers is via an HDMI connection, optical audio, optical coax or, less common, some other device splitting out the 5.1 channels of audio and then each getting pumped into 5 sets of jacks (one for each speaker).

If you DO want real 5.1 surround sound, I think vipergts gave you the best input above. Maybe shift this system to some other purpose in your home (perhaps a bedroom stereo purpose?) and buy yourself a more modern surround sound system?

You can get pretty good ones for not much money. Or if money is not really an issue, consider buying yourself a good quality AV receiver and new speakers.

The receiver would then own the various device inputs (not your TV) running only a single HDMI cable from AV receiver to TV for picture output. Sound would be 'owned' by the receiver for everything you want to connect to it and it would deliver real 5.1 or stereo based on whatever source of sound is fed into it. That's the BEST way to go if money is not really an issue. Fake surround is not a great substitute for real 5.1 surround. Your ears would very likely notice if you went this way. Else, if you don't care, the hookup suggested by al2teach appears right. But you'll never get real surround sound with that hookup (instead, the Bose will be faking the surround by sending some parts of the audio to each speaker.

Just not necessarily the right parts). Lastly, if there is a digital audio input on the Bose (my guess would be digital optical), then it probably can play real surround but only if digital audio enters it through that jack. Apple made the wonderful decision to jettison the optical jack from TV4 so if your Bose system has that as the only option for digital audio input, you'll need to look at approx. $30-$60+ little boxes that are basically HDMI audio splitters: HDMI out of TV and into a little box which then splits the audio signal out to an optical digital audio out jack that could be connected to an optical digital audio in jack on another device. Amazon has many of these kinds of boxes. But, again, this only works if your Bose box has an optical audio in jack. I hope this helps.