I'll try to answer this one.
Lets use your spring example. When you compress a spring and let it go, it will expand and then contract again. This movement will get less and less until the spring is stationary. That's because it's losing energy through heat loss and friction. If, however, it was a 100% efficient spring, it would continue expanding and contracting forever, since it's not losing any energy.
Now, say you apply 2 lb to the spring to compress it, that is the energy you're transferring to it. If you have a less efficient spring, it will come to rest quicker. If you have a more efficient spring, it will take longer to come to a rest. But the 2 lb and thus your energy transfer remains the same regardless of how well the spring uses the energy.
Same with a bow. For argument sake, if you draw 100 lb that is how much energy you will transfer to the arrow. The arrow only determines how well the energy is used. So if you have a weak or stiff spined arrow, there will be more losses due to friction, etc. because the arrow isn't flying as well. But the 100 lb is the same, regardless of the arrow! That is also why a heavier arrow will fly slower than a lighter arrow. It's the same force applied to two different weights, so it would be impossible for them to have the same velocity.
I hope this makes sense and doesn't confuse you even more.