"You can never remove more damage than the creature currently has. Any excess healing or regeneration is lost."
Bleed: "...Whenever this creature...heals...you may remove 1 Bleed condition for each point of healing you cancel"
I would say that you can use healing to remove bleed, because it says that you cancel the healing (a specifically defined effect), not the damage removal (a more general result of healing).
Cancelling a spell prevents it from resolving. Cancelling a point of healing should prevent it from resolving as well. If it did resolve, it would be lost, but since it was cancelled before resolving, it still counts as being cancelled, and so you can use it to remove bleed. I think the key thing to notice is that nowhere in the heal effect does it state that an uninjured creature may not be healed, only that if it is healed, you cannot remove more damage than it has.