Are there any exceptions to the first precept? I recently accidentally injured a bee, I did all I could to help it, but its wing was broken and so was its leg, it could not walk nor fly, it was clearly in a great amount of pain and distress. I tried to heal it with some energy work, but it was no good, I am just not experienced enough and for some reason on that day couldn't find focus with my energy work.

So I took the decision to do what was necessary to stop what I took to be unnecessary suffering, I killed the bee.

In another occasion where I was not responsible for the initial injury, I found a bee in great distress on the ground, I am not sure what happened to it, I think maybe it stung somebody because it appeared very hollow inside. There was nothing that could be done for it, and though it gave me great sadness, I also killed this bee to end its suffering.

I love all life, it greatly saddens me when I accidentally kill something, and even more so when I have to do it knowingly. But it would sadden me even more if I had to leave a being in suffering and not doing anything when I could and there wasn't a reason not to.

Am I breaking the first precept or can an exception be made to end the great and unnecessary suffering of a being who cannot be saved from their fate?

I heard a story about one of Buddha's previous lives where he sad that he found out about a murderer on a ship who was planning to kill everyone, and out of only compassion for the man the Buddha killed him with no hatred and only love so that he wouldn't have to go through all the terrible rebirths fore his actions of killing everyone on the ship (this is from a memory of someone telling me this story, I believe that they had read it somewhere, but I may be getting some the details wrong). And that by doing so he in fact cleared a huge amount of previous karma, rather than gaining any for this act. That is not to say though that I am doing this with the intent to clear karma, I merely want to help the bee.

Now although that is a different situation, could that be related at all to this?
Don't beat yourself up over it.  Precepts are an interesting thing.  Most people come at them with the idea that they are iron clad laws governing our behavior.  Don't get me wrong, in some ways they certainly are.  When you take this kind of legalistic perspective, however, I really think you are missing out on their greater purpose.  

The precepts are decidedly simple.  Abstain from killing.  Abstain from stealing.  And so on and so forth.  But what does it mean to kill?  Did the Buddha really say steal?  The Pāli reads more like "do not take that which is not given".  What does that mean!?  Likewise, anyone with an opinion will give you their interpretation on what the "sensual pleasure" precept refers to.  Reading the precepts this way isn't to split legal hairs or an attempt to loosen restriction.  These are all valid and important questions - questions I think the Buddha intended us to ask by making his training rules so brief in content.

Rather than view the precepts as moral law, it might be helpful to see them as a kind of spiritual Rorschach test.  What you see is very much dependent on where you are in your spiritual development.  Please don't take that to mean that the more ironclad you are in your interpretation, the more advanced you are in your training.  The precepts are factories of insight.  They are meant to teach and enlighten not just govern behavior.