Skipping the bombs means skipping the only item that Link can used to damage himself, and also the only item Link can carry that allows for ledge clipping. By skipping bombs, skipping the Trials and getting to the last platform before Ganondorf without the hookshot must be done differently than usual. Although there are several methods for skipping the Trials without bombs, getting to the last platform without bombs is much harder due to there being very few ways to take damage in that room.
A roll clip to skip the trials from the lower level is possible with nothing but the Deku Leaf. To do this you need to grab the ledge so that practically all of Link's left hand is in the wall. This works for 2 ledges: on top of the door frame or on the ledge next to the door.
On top of the door frame:
Next to the door:
It is possible to skip the Trials using a skull roll clip. This method works the exact same way as the more common Bomb Roll Clip method for Trials Skip. Put the skull near the ledge but not completely against the wall. With the leaf, grab the ledge in between the skull and the wall. Tap towards the skull to do a partial ledge clip and climb up. Then perform a frame perfect roll clip, and leaf pump your way to the loading zone to skip the Trials.
It is also possible to skip the Trials by using a series of tricky item slides. First, item slide to a door frame and then item slide to the horn above the Trial Door to grab it. You can then jump and grab a ledge to get on top of the very large door frame. On that door frame, there is a slope on the right side that you can clip through by item sliding sideways into it. This will make you fall down inside the door frame. You still don't quite have access to the loading zone from there, but there is a tiny gap in between the door and the wall, which you can item slide through to hit the loading zone.
Normally, entering the Ganondorf fight requires the hookshot. However, the hookshot, being in Wind Temple, takes a very long time to obtain. It is possible to skip it using the Zombie Hovering glitch. Not having bombs means that the hover can't be started with bomb damage, making any hover a lot harder.
First, stand close to a morth, and then stab it (forward + B) so that Link will kill the morth and it will attach onto Link at the same time. (This sets the flag for the morth to drop a heart when it dies, which can only be activated if Link kills the morth with his sword). Now Link can shake off the morth with a roll (the direction of which is random, but will always be somewhere behind Link), and use the Leaf to blow the morth up onto the platform which has the loading zone to the Ganon fight. After the morth has been shaken off though, Link cannot move at full speed as this will causes the morth to try and move towards Link. This is advantageous after the morth is already up on the platform however, as it can be used to position the morth wherever you want.
For this method, place the morth anywhere on the platform, but make sure he is pretty far back. Get into position on the left side of the warp pot, facing the final platform, and with the bow aim at the edge of the yellow texture to get the correct angle. Walk sideways left (the morth won't move) and press B to perform a mid-air jumpslash once you slip off. This will make you jumpslash down, recoil against the middle level and land at the bottom of the structure, near the chain. This way, you will take fall damage as you land, skipping the need for blowing yourself up with bombs.
Then, perform a jumpslash (5 frame window) and mash B to Zombie Hover. You will need very good mashing in order to get up to the left side of the platform. Grind against the left pillar to get to the top and then grind against the ceiling. Because the recoil of the jumpslash gave Link 27 speed, decreasing by one unit each frame, the morth will have moved during 12 frames while you were taking fall damage, and so the morth won't be where you left him exactly. Grind against the top of the platform until you are right above the morth. Then stop mashing and press the bow button twice (once to pull out the bow and once to shoot an arrow). If your second bow press was done frame perfectly, the arrow will kill the morth. Immediately mash B again to zombie hover (make sure you didn't fall under the platform), and pick up the heart. Proceed to the Ganon fight.
The reason for the mid-air bow snipe is that shooting the morth before starting the hover would make the heart disappear before you can get to it.
Instead of taking damage with bombs or fall damage, you can take damage from a morth on fire. Place a morth on top of the final platform after doing the stab trick, place a morth under the platform (you can use pots to push the morth around), then go in front of the ledge morth, and align yourself with the one that will drop the heart. Shoot the morth on the final platform with a normal arrow then the morth right in front of you with a fire arrow. This will cause you to take damage and make you slide back slightly. You can then hover to the heart.
In Puppet Ganon's chamber, angle yourself towards the path that leads to Ganondorf. Deminish you health to 1/4 heart and zombie hover. This is a mostly luck based hover, as the conditions have to be perfect in order to prevent from getting knocked down by the Keese. Once you are above the red wooden entrance to the Ganondorf battle, wait for a few Keese to come and attack you. In order to survive the hover, you will need to kill a keese while hovering and get the heart they drop. Without bombs, the only methods are by either sniping a keese in mid-air with the bow, or by using the boomerang.
There are several reasons this hover is exttremely difficult and most likely not RTA-viable. First, you must take damage using Puppet Ganon's attack since you don't have bombs to damage yourself. This already isn't reliable because Puppet Ganon's movement in the room is RNG, and your angle can very widely change from where and how he damages you. Then comes the hover. Even with perfect mashing, sometimes the keeses will come down before you can make it to the final platform, and they can randomly hit you all the way down. To this, also add Puppet Ganon's random movement in the room, which can push you around and make the hover impossible with bad luck. Finally, sniping a keese with the bow requires a random keese to go right in front of Link, and the bow shot is frame perfect.
With the boomerang, you can target the keese you want to kill, making this a little bit easier, but still insanely difficult.