Create targeted modal website overlays promoting your resource and pop it when the reader tries to exit your blog. You can target only those readers that are engaged but have not yet subscribed to your newsletter.
Provide download link to the resource in exchange of a valid email address.
You have a long list of email ids of otherwise anonymous readers. You have a spike in the number of downloads of your resources. You have a decreased Bounce Rate. A win-win-win situation for you.