This exploit can be used with any of the Boss Souls you acquire after defeating a Boss. You can avoid patches being installed by disconnecting from the internet until you are ready for the game to install new patches. To avoid not being able to use this exploit, either do not install new patches before using this exploit or delete the patches. Note: This exploit was performed on patch 1.04 of the game.
Additionally, equip the Covetous Silver Serpent Ring to get even more souls between rests at the bonfire. This increases the amount of souls you gain for a limited time, but you have to be embered for this to take effect. After you ember yourself, use a dried finger. To get more HP and survive longer, ember yourself while doing this. This can be done with any bonfire to respawn enemies. You can kill them again with minimal difficulty and work your way back to Firelink Shrine. Then, teleport back to the first area and all the enemies will have respawned. Thus, once you reach the Firelink Shrine, use the bonfire.