If the Super Secret Room mimics The Womb, he will drop red hearts instead of soul hearts, then gobble them back up. This can be avoided by allowing Dark Bum to pick up all of the red hearts and then quickly exiting the super secret room before he starts dropping hearts. This way, he will drop a considerable amount of soul hearts.
Keeper - Does nothing, since there's no heart pickups in Keeper's run.
The Forgotten - Makes it harder to keep The Forgotten's bone heart containers, since every red heart on the floor will be collected and transformed into soul hearts, which can only be used by The Soul.
Prior to Version 1.02 Dark Bum's red to soul heart conversion rate was 1:1, but it was set to 1.5:1 with Version 1.02.
Prior to Version 1.031, Dark Bum did not have a chance to spawn spiders of either kind. This was likely done to nerf its use with characters that start with no or few heart containers.