I haven't followed the steps given, but having paper bills shouldn't prevent you setting up a BT ID and certainly not getting BT Sport online. Can you detail where it's going wrong?
Well the legal stuff section currently says
BT Sport Online – UK residential broadband customers only. BT broadband customers can watch BT Sport online at home with a minimum line speed of 400kbps. To watch BT Sport online elsewhere you need 3G/4G/wifi (charges may apply). To watch BT Sport at btsport.com you need Microsoft Silverlight. The BT Sport App works on iPhone (3GS and above), iPad (iOS 5.1.1 and above) & selected Android devices with OS 4.1. Max. 2 devices simultaneously. BT Sport is free for new and existing customers. Major League Baseball not available online. e-billing required. e-billing required. UK only. Terms apply.