Healing bomb uses a bomb and either a cure extract or a cure potion.
Fast bombs lets you throw up to you number of attacks in bombs.
Can you throw multiple healing bombs? It is potentially even better with haste.
Rules as written, I don't see anything wrong with it. It feels a bit munchkiny to have the alchemist out-heal the cleric, even if it is just for a round or two.
Is this just good resource management or do I have stinky cheese on my hands?