iPhone 6 bluetooth- how to play while on phone, if possible?

Hello all!

I cannot for the life of me figure out this, but maybe it's because it's not possible. On my old simple feature phone (which wasn't even a smartphone) I could be on the phone, and listen to music thru my bluetooth speaker system in my office. This is important because my phone serves as my main system for the waiting room etc, at the computer store I manage. Whenever I get an alert or a phone call, the music stops and when I answer the phone the music doesn't continue, yet the phone itself is what I hear the caller on, not the speakers above me. If I toggle the music back on while in a call, I hear it thru the same phone speaker, which to me is pointless. When I go to the speaker switch menu, it only allows me to choose "iPhone speaker" and not "Bluetooth/Bose"

I know this is possible because I've done it with other phones. I'm not sure if I'm missing something or if the iPhone lacks this ability. How can I reserve certain alerts and noises to the phone itself (when I get a call the ringtone is on the sound system, as well as clicking if I'm answering an email or text, even if the phone is toggled to silent). I also would like to keep the music playing, after all, it technically isn't playing thru the phone, so I'm not sure why it is stopped completely.

I don't think I've done anything wrong with the setup of my phone, but I guess there could be something awry. If any of you has any input, it would be greatly appreciated.