As for ringing the bell, I have had a TON of success with this method, as have my students. My "method" addresses getting the dog to make the leap, as well as "mis-rings".
Teach the dog to target your hand first. When that is reliable you can move on to the bell.
Put your hand behind the bell on the doorknob and ask the dog to touch. The dog will have to push through the bells to get to your hand. As the dog gets more familiar with this step, I begin to change the word to "Bells" or "Out", so that I can reserve my "Touch" cue.
When the dog does this, immediately whip open the door and run outside with a lot of fan fare.
I do this every hour, often seeing the dog touch on their own in 24 hours. They know what is coming and dogs love to anticipate and rush ahead of cue. This is using the dogs tendencies to our advantage!
As the dog realizes that touching the bells gets you up and gets them out, they may start to ring just to go out and play. In the beginning, HONOR those rings! This is very important. Most people need to use the bells because their dog had no way to signal the owner, or the owner could not read the signal the dog gave. DO NOT squander this brand new communication by telling the dog no!
After about one to two weeks you should start to be able to see a pattern. Use a notebook if you have to so you can track times of eating, drinking, ringing, pottying, and playing.
If the dog rings the bells and then does nothing outside, come in and go in the crate for a few minutes. Just a brief time out to reinforce what the bells are to be used for. After a few applications of this step, I rarely have dogs ring for nothing. Sometimes I do like that my dog rings them if she really needs to go outside to see something or play. I personally LIKE that level of communication.
Although my dog no longer needs the bells, I keep them up. From time to time she reminds me that she needs out. From time to time I still ask her to ring before I'll let her out. For me, this makes it a lot easier to transfer to a different place. Dogs may know it is not okay to pee in my house, but not a different house. By putting the bells on a doorknob it seems to help her make the jump to "Oh, that is the door to take to go pee. Can't pee here!".
All other potty training rules will apply, such as watching your puppy like a hawk, crating, tethering when you can not watch them, etc. This just helps me speed things up a bit.