I love this little "service counter bell" that one of my clients has, which her dog would ring in order to ask to be taken outside to potty. (My dogs were taught to ring some jingle bells). The bell sits on the floor by the door, which avoids the issue of the jingle bells ringing every time the door is opened or shut. I cleverly thought I could avoid the roughly $25 cost of the "Tell Bell" by buying a $5 service bell from Office Depot and super-gluing a fabric button onto it to give the dog a larger spot for his paw to hit (the normal service bell has a very small button to push and I suspected my dogs would object to pressing it with their paws).
After much struggling with it, I have given up because the surface area of the little button isn't large enough for me to get the glue to stick. The Tell Bell has been made with a larger button to push (and it has a cute paw on it). So I am recommending it for my clients who would like to teach their dogs to ring something to ask for a human to open the door.
You can teach this behavior using "target training". You teach the dog to ring the bell to get a treat. Then you can use "back chaining" to create the sequence of (ring bell) (human opens door) (run to potty area and do your business) (click/treat).
The toughest part of this sequence is getting the dog to not ring the bell just to be able to engage you in training. In other words, they sometimes lie and make you go through the routine even when they don't have to go outside. If I feel I've been faked out, I just calmly go back inside (ie, no click/treat). But I'm generous in nurturing the behavior until it's very solid-- in other words, I allow myself to be taken advantage of until the very advanced stage. I'd rather err on the side of being asked to open the door than have to clean up an accident.