For some reason it is not possible to buy Dark Souls 1 for xbox on your console. Meaning if you start your xbox and head to the store it says that it is not available. But it's in the store listed as backward compatible
However YOU CAN buy it on xbox.com. Just as you can buy any other backward compatible game there. I bought the game this weekend on xbox.com. After my purchase I could see it on my Xbox one like any other game. When I went to the store on my console it now said "play" instead of not available.
When I tried to start up the game the first time I had to log in. It would not accept my regular password. It turns out that you have to create an app specific password to access your new Xbox 360 game (at least I had to). Basically you go to your live account and create a new app password. Then you use this for your login.
I hope this helps someone out there :)