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As far as warping space and then traveling the shorter distance goes, yes it is possible. Any object in space with a gravity field, including planets, stars, and black holes, all do that to some extent, with black holes being the most noticable out of them. What is required to bend space is a large gravity field. The larger the gravity field, the larger the warp in space. In order to bend space enough for us to travel a distance that would require faster than light travel in non-warped space while still traveling at sublight speeds would require a massive gavity field, much larger than the one produced by our own sun. Even if we could create a field like that in theory, such as using gigantic electromagnits for example, it would require huge amounts of energy that we're not capable of producing at this point in time. Thus, it is extremely unlikely that we will be able to warp space using gravimetric fields.
But then, that's just one theory on how to approach it, and there are many others. Just because one theory won't produce a likely result doesn't mean another won't. NASA has a laboratory, sort of a think pod, that is devoted to finding faster ways to travel. Solar Sails and other such ideas are floating around out there as well.
Just remember, nothing is impossible, only highly unlikely.
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