Your reading list may already be linked to your module NILE page, you can check this by navigating to the module page, selecting 'Reading and resources' and checking if the reading list is listed. If this is not the case:
For Blackboard Original, navigate to the 'Reading and resources' page in editing mode. Click 'Tools' and 'More tools' then select 'Reading lists'. Enter the module details and click submit. The reading list should then be embedded on the NILE page.
For Blackboard Ultra, click the add content (+) option and click 'content market'
Scroll down to 'Reading List' and click the plus icon (+) on the bottom right corner
Your reading list will appear as 'hidden from students', click this and open the reading list to link it.
If you didn't already have these, you will now have editing rights on the reading list.