How can I be sure the bananas I purchase are of superior quality?

By their color. Avoid bananas that appear gray and bland. Chances are they were refrigerated, which  effectively stops ripening it its tracks--for good.  Yellow bananas with flecks of brown or black are ripened bananas. If you plan to eat bananas the day of  purchase, go with yellow. If not, select bananas that are slightly green and firm--signs that full ripening has yet to occur. Slightly green bananas generally ripen within one to three days. Avoid bananas that are bruised or discolored. 
 
Source(s):
Dole.com "Bananas"
Banana.com "How to Purchase"