You don't draw a bowstring and then release it (also known as 'dry firing') without any arrow because it could cause both the string and the limbs of the bow to snap. The reason: shock from the rebound travels back into the structure, unlike when an arrow is fired where the kinetic energy gets fully transferred into the launch.
That "fully" bit seems very unlikely, but I'll believe the overall gist of it.
Bows transfer about 65-89% kinetic energy from the elasticity of its limbs to the arrow. Compared to guns which only transfers about 30-34% of the potential energy in the gunpowder to bullet, it's comparatively much higher.
The rest of the lost energy was mostly absorbed in the arm of the shooter of the bow itself, and neglectible amount was spent by the string for cutting through air resistance. Compared to guns where there's various mechanisms like the rifling, the blowback and other parts that spends the rest of the energy not transferred into the bullet, so it's not a total net loss.
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