Your Spacebow (Probably) Doesn't Work
Such a process isn't scientifically possible by any science we know of. However, there are some hypothetical models based on relativity that do similar things. Like enable FTL travel via warp drive engines.
The problem here is that "warping space" just moves the object with respect to something else by adding or removing space between the two objects. To my knowledge, it doesn't add or subtract momentum from the object in question. So when you release your spacebow, the projectile will simply return to its original position and sit there.
Another Form of Spacebow
An actual bow and arrow will work just fine in a vacuum. In fact, they'd work better in a vacuum since they aren't slowed by air resistance (so they hit the target with as much momentum as they left the bow, as opposed to normal arrows that slow down with distance). But really, it seems kind of silly for a group of people capable of warping space to be using primitive weapons for anything but sport.
Still, if you just want it to be cool, there's nothing wrong with a half-mile megaspacebow made of some kind of carbon nanotube springs that launches a projectile at relatively high speeds.
Just realize that it's not nearly as effective as putting a couple tons of conventional rocket fuel behind it.
Something done defensively in Killing of Worlds is gravity hills. This involves artificial anti-gravity (also not scientifically possible under current theories, but remotely plausible for future science), where they create these areas of intense anti-gravity around their ship, so incoming projectiles "climb the hill" until they lose most or all of their momentum.
You could potentially drop a projectile down the "hill" and accelerate it to high speeds this way, but the energy would undoubtedly be better spent just accelerating the projectile through more conventional means. However, I could see it being used defensively, then the ship just dumps a few hundred tons of ball bearings in front of the gravity generators to blow holes through the opposition.
Now, relativity models gravity as a form of space warping. Under this model, antigravity would be a way to warp space "the other direction". I don't know nearly enough about relatively to say more than that, but it sounds less hand-wavey than your spacebow. Although not necessarily as cool.