Entering the Bottom of the Well is an important stop for many routes because it contains the most easily accessible bombchu chest.
There are three practical ways of entering Bottom of the Well without draining the water out of the well, and one impractical but interesting way. Typically, one would activate ISG off a cucco and dive in the well that way. If one doesn't have a shield, ISG is not possible so damaging the cucco with jumpslashes is preferred. If Navi appears, one can simply Navi Dive.
The quickest method is to activate ISG directly off of picking up a cucco. Alternatively, one can activate ISG off of a sign, put away one's equipment and simultaneously roll into and grab a cucco.
Once the cucco is overhead with ISG active, make your way to the edge of the well and face away from it. From here, shield drop the cucco and backflip immediately afterwards to fall through the water during the cucco rage cutscene. Once you regain control of Link, quickly make your way to the Bottom of the Well entrance.
Do not backwalk with the cucco above your head as there is a high possibility of raging the cucco prematurely. The cucco will stay above your head indefinitely no matter how much you walk around normally.
In some scenarios, you may want to get the Deku Shield from the chest in the Bottom of the Well rather than the forest, which means you cannot activate ISG to reach the entrance. In this case, one can damage the cucco beforehand and jumpslash the cucco when it is on the edge of the well.
This method is notorious for being difficult to perform quickly as you must do a minimum amount of damage to the cucco to ensure you make it rage on the final jumpslash. Typically, two jumpslashes should provide adequate damage. Then, one must throw the cucco onto the edge of the well, and jumpslash over the well so that you fall into the water and rage the cucco at the same time.
Simply perform exactly the same set up as escaping the Forest using a Navi Dive. The true advantage of using Navi as opposed to a cucco is that one can Navi Dive at night - when the chickens are not present.
This method is completely impractical for a speedrun, but is still of technical interest. Before starting, it is useful to throw the chicken nearest the pathway to Death Mountain Trail right against the wall so that it is easier to pick up later.
Clip into the out of bounds into the house behind the Potion Shop by jumpslashing into the acute angle corner at the top of the stairs. Jump over the gap in the floor and pick up the cucco on the other side of the wall. Jump back over the gap in the floor and align yourself with the Bottom of the Well entrance which you will be able to see. Jump in its direction, whilst avoiding going back in bounds at the bottom of the ladder you initially climbed up. Manoeuvre yourself to hit the loading zone of the Bottom of the Well.