I have great insight into organic bananas as they are a permanent guest in this house.
Non-organic bananas are dipped in a nasty chemical whole that sinks through the skin and into the fruit and makes them ripen at a predictable, even and slow rate.
Organic bananas are a different animal. I find that if you buy organic bananas too green they might never ripen. I've had this happen most time that I bought organic bananas very green. Look for bananas that are starting to turn at least a little yellow. Also, when a normal banana looks like it would be too green, an organic banana that looks the same might be ripe. Organic bananas can go more quickly from unripe to too ripe compared to the chemicalized ones. That's why they put the chemicals on the fruits to begin with.
I don't believe that they can irradiate fruit and still call it organic, but I'm not sure about that. Even if they do, you are still better off with organic because of the dipping juice they put non-organic bananas into.
Try again withe bananas and keep on trying until you get the feel for them. Most fruits need to get to be known for awhile before you can understand how to pick good ones and how to know when they are really ripe. I've gone through this process with avocadoes and mangoes etc. When you switch from non-organic to organic bananas, you have to go through that same process.
Mama Sutra - do you really mean that until just last year you didn't eat bananas? I'm curious how that can be, especially if you lived in Hawaii!!!
Greenbunny