Bose is not an "upgrade" from even an average home speaker and I guess your BF is not up to date as he might think. Not only are they not making those tiny crap home speakers anymore, they were never good for music to begin with. Guessing you didn't choose him for his audio gear knowledge
Mix out looks to be your only option, though since the sub does not have speaker level inputs and the receiver doesn't have an actual sub preamp output.
Standard RCA cable that you can get anywhere if you don't have one laying around. The cable used for the CD player is the same thing, if you have one of those.