Ok, I know this is a year later but I just ran into this problem. I have a JBL Charge Speaker and I accidentally and stupidly hit "forget this device" in Bluetooth settings on my iPhone 5 thinking this would allow someone else to connect to the speaker when in reality all you have to do is turn off bluetooth and set the device to pair mode and it would allow the other device to connect.
Now there's a ton of people who are resetting network settings or even going back to factory defaults on their phones or iPods. I thought to myself for a second that there is no way that I am resetting my phone and why can't I reset the speaker because it's basically just a brick with zero settings to restore. So I reboot my iPhone (for good measure) then turned on the JBL Charge which put it in pair mode and then held down the power button on the Charge for about 4 seconds and it beeped and the lights flashed red and then I looked at my phone and the JBL Charge reappeared in Bluetooth settings and I was able to connect again.
So my recommendation is to do everything you can to try reset the bluetooth device before taking the hours it takes to restore your phone settings.
- Aaron