Skipping the Hero's Bow is by far the most difficult item to avoid. Even if you manage to skip the bow in Tower of the Gods, you will still obtain it once you obtain the Fire and Ice arrows and Light arrows. Therefore, you must skip the bow in Tower of the Gods, and all enhancements associated with it.
Also note that if you wish to skip the bow, deku leaf skip is no longer an option. Currently there is no known methods to skip the Light arrows without using the leaf
The only requirement the bow has in Tower of the Gods is shooting the eye switch in the room right after obtaining the bow itself. Shooting the eye reveals movable platforms, which can then be used to carry the second statue across the gap into the central room.
This can be avoided with the use of chest storage. First, obtain chest storage in the first floor or from the tingle chest. Then, after you collect the second statue and carry it to the room where the bow is normally required, use chest storage to navigate around and through the pillars to carry it across the gap.
Normally to defeat Gohdan you must use the bow to shoot the hands and the eyes to be able to reveal his mouth which you then throw a bomb to deal damage. However, bombs also damage the eyes and hands, and can be used exclusively for the entire fight. Throwing the bombs at the hands and eyes is easier said then done though, as their movement is random and the bomb throw timing is precise.
It should also be noted that because you never obtained the bow, Gohdan will continuously snot out arrow pickups, as he thinks you currently have 0 arrows. This makes it extremely difficult to time the bombs and deal damage. This can be avoided by obtaining an arrow upgrade from either Western Fairy Island or Thorned Fairy Island. These upgrades do not give you the bow itself but set your arrow count to 60, so Gohdan will not snot arrows constantly.
In order to skip the Fire and Ice arrows, you must obtain the Power Bracelets and Iron Boots without their use. It should also be noted that this is only possible on the Japanese version. If you attempt to enter Fire Mountain or Ice Ring Isle without freezing or cooling them on any other version you will void out immediately upon entry.
To get into Fire Mountain without Ice arrows is fairly straight forward. Just start a hover from the edge of the island and heal with either a heart drop from the Kargaroc or with the tingle tuner. If you timed healing correctly you will fall into the hole and be able to obtain the Power Bracelets.
Getting into Ice Ring Isle without Fire Arrows is one of the most challenge portions of the bow skip. To do so requires Door Cancel, so you will be completely blind for the entirety of the skip. You will also need a lot of height, so you must start a zombie hover from Southern Fairy Island or another close island. Once close to Ice Ring Isle, heal yourself with the tingle tuner and leaf to the loading zone very precisely, as it's still very easy to freeze and void out.
There are several ways to skip the light arrows. Only one of them is fitted for low% though, because the bottle and the boomerang are also skippable.
Head over to the room on the right that leads to the Phantom Ganon battle and wait for the cutscene to finish. Head over to the left near the drop off by by the stone. There is a little indentation which when you run towards will allow you to jump without falling into the Phantom Ganon battle. Once you have found this spot, run off it and use the deku leaf to get on top of the stone.
Set a bomb down and then pull out the wind waker and cancel it so that it is still in your hand. Now here comes the tricky part, getting a wind waker dive off of the bomb followed by dry storage. Sometimes you can simply flick the control stick towards the bomb at an angle and mash the button your wind waker is on to get the dive. Once you have gotten it, cancel the wind waker just in time to get dry storage (pause buffering may help with this).
Store the text from the stone and run back over to the door. As you press A to open the door, the text from the stone will pop back up. Quickly mash through the text box to keep the door from closing. Now run over to the door on the opposite side of the room, watch the cutscene, and return to the preceding room. Run through the open doorway and leaf pump to the loading zone.
You can also skip the cutscene in the dark portal room by getting storage a second time on the stone tablet.
Because you are required to use the Deku Leaf to skip the Light arrows, the Deku leaf is not skippable if you wish to skip the bow.
One of the consequences of skipping Light arrows is you have no way of killing Puppet Ganon. Therefore, as a conclusion to the bow skip, Puppet ganon skip must also be completed. See here for how to skip him.