As Bunny Link, there are several glitches you can use to regain control of Link without gaining the Moon Pearl.
This is a state where the player is not completely Link but has gained some of his abilities. Ordinarily the Bunny cannot dash, use sword, open chests, pull objects such as levers or rupee trees, or pickup and throw objects, but super bunny can. The Super Bunny still has one of the main restrictions of the Bunny state though: it cannot use items other than Magic Mirror and Bottles. This state is lost if the player takes damage, bonks, or transitions between the overworld and the underworld. There are a few ways to gain this state:
Fall Through a Hole
If the player falls through a hole that has another floor below it, Link will be Super Bunny on the new floor. An example of this would be entering Skull Woods as bunny and falling into one of its entrances. Link will be super bunny inside the dungeon.
Dark World Fake Flute
Talking to any NPC who gives the player something (such as the Fluteboy or the Bottle Merchant) will give Link Super Bunny status. Other NPCs, such as the bully and his friend on Death Mountain, will not give super bunny.
Mirror Transitions to Underworld
By mirroring on the same frame Bunny Link enters a house or cave, the player will become Super Bunny inside. This is used in Defeat Ganon speedruns to get the 300 rupees in the House in Village of Outcasts while still Bunny Link.
Link Without Moon Pearl
There are also a few ways to get normal Link in the Dark World without the Moon Pearl. In this state, you will be able to do everything Link normally can, however, if the player enters the underworld (or is already in the underworld when the glitch is activated) and exits back to the overworld, Link will be a bunny again. An exception is made if the player exits to the Fake Dark World, where the player will retain control of Link and can freely use all entrances to the underworld on the screen. But if the screen is transitioned on the overworld, the Light World will be loaded.
Below are the ways to trigger this glitch:
Dungeon Bunny Revival
Dying in a Dark World Dungeon as Bunny Link will make you respawn at the entrance as normal Link. If this is done before Agahnim 1 has been defeated, the game will be in Fake Dark World. If done after, it will remain in the Dark World.
Water Bunny Revival
Using a bottled fairy, Bunny Link can be revived as normal Link if he's over deep water. This is easiest to do if the player also has the Flippers.
Super Bunny Pull