By using an Ice Rod Clip in the cave between the overworld and Swamp Palace, you can reach the loading zone underneath the water without lowering it, which effectively skips using the Big Bomb Flower.
This is done by merging along the wall in the cave until reaching one of the square torches in the northern corners of the room. Unmerge onto the torch and put it out by either slashing at it or using the Tornado Rod. Then line up an Ice Rod block so that it is right up against the edge of the torch. Then QE-Cancel your shot and get underneath it as quick as possible. To successfully get to the loading zone is a bit tricky as it seems you need to face towards it before the actual clip happens otherwise Link will just fall into void.
Skipping the Big Bomb completely is not worth it in 100%, because of a Maiamai right next to the Big Bomb, as well as the rock in front of the cave with the Rupee Fairy in it still requiring the Big Bomb. Regardless, there are some ways to acquire the Big Bomb without purchasing it.
Using a Ropa to push Link into the southeast corner where the fence and trees meet, it is possible to clip partially into the fence. From there, a Hookshot Clip can be performed on a bush to get inside the fenced in area with the Big Bomb. Doing so allows you to use it without paying the normally required 200 rupees.
This is the only used method of skipping the Big Bomb payment as all other methods are too slow.
Using a Ropa, it is possible to clip through the northeast part of the fence surrounding the Big Bomb.
The current setup is too slow to be worth implementing in a speedrun.
With the help of a Lemon Boost (Nice Bombs only) or a Fire Rod Boost (difficult), you can get on top of the wall south of the Octoball area, and carefully make your way on top of and inside trees until your reach the trees right next to the Big Bomb.
The current setup is too slow to be worth implementing in a speedrun.