With help from Fyer, you are able to reach the distant Gerudo Desert.

Go to the Bulblin Encampment

At the desert, there will be a cutscene. Afterward, make your way toward the golden spires in the distance. Near a fire, you will find some Bulblins and their Bullbos. Kill the Bulblins and ride a Bullbo through the fences that block the way north. Go up the stairs and keep going north to reach the Bulblin Fortress.

Bulblin Fortress

Make your way through the fortress, looking ahead for Bulblin guards. Try to shoot the guards before they can see you. One of the guards will be holding a key. After you get the key, hit the roasted Bullbo nearby to get a piece of heart. Open the chest in the corner to get a purple rupee. Then unlock the nearby gate that you passed on the way here and do a roll attack on the gate to open it.

The gate will close behind you after you go through. Approach the Bullbo, and King Bulblin will attack. Hit him with your sword until he falls. After a cutscene, climb onto the Bullbo and use it to crash through the gate that you unlocked a moment ago.

After another cutscene, dismount the Bullbo and go straight ahead into the Arbiter's Grounds.