I am no software engineer, but I found out a way of reading Bloomberg articles after reaching the free limit.
1. Click the page ARTICLE YOU WANT TO READ.
2. Click Esc to stop loading content immediately after the page opens ( I'm assuming whatever magic is responsible for blocking your access is loaded after the text)
3. READ your article.
I by no means encourage others to take these measures, but I understand that I must divulgue such a loophole :D Unless Bloomberg know already and are doing us a favor.
Or, use the excellent uMatrix browser extension to block cookies and JavaScript on bloomberg.com. Blocking cookies and/or JavaScript works for getting around the paywalls on many other sites, including the NY Times, Washington Post, etc. On some sites, you can view paywalled pages simply by going into "Reader" mode in Firefox.