If you take the main road in this zone, the one that follows the eastern side of Red Mountain, you’ll end up passing by the dungeon’s entrance. There is a small wooden door in the rather large boulder, just next to some boxes, close to the main road. This is where you need to go, to find and talk to Bulag Idolus as a part of the main quest. Bulag is found on the first large platform, close to the entrance. During the first interaction with her, you’ll choose her fate. You can either spare her life or kill her.
While in the Bandit’s Cave, we need to find a cozy part of it. This small portion is located in the northern part of the delve, not including the front entrance tunnel. While inside, keep to your left all the time. You should spot it after the first crossroad, several steps further inside, on your left side. The cozy part becomes immediately recognizable. The owner of this spot has decent taste, and it feels like the most fun part of the cave.