As you mentioned, there are no examples using a LightBlue Bean. However since it is a BLE device I don't see why wouldn't it work with an Edison. Unfortunately I don't have access to one so I can't test it. However I'd suggest you to start by reading section 6.1 of the Intel® Edison Bluetooth® User Guide. In that document the Edison's BLE capabilities are explained, I believe you might find it helpful.
Do you get the connection between beans and edison? I need to do exactly this, but I have no idea on how to do that.
I pair and connect both devices via edison's serial console but I don't know what to do after that.
Hope you can help me.