The well will take you down so you can get into the water that leads to the Dragon's lair. You might want to take the bucket along with you. To do this, you will need the dagger. Use it on the handle of the bucket to cut it free. You must be sitting in the bucket to do this. Once you cut the bucket free, you and the bucket will fall into the water. Grab the bucket and dive by using an action on the water. Keep in mind, once you cut the bucket free, you can not climb back up the well (not that this will be a problem).