OK, here's some more science stuff.
And on this occasion it's real science, too. Hard as it may be to believe, the slingshot maneuver has actually been accomplished with unmanned space probes headed for the more distant planets or beyond. It works about as described in the story. Of course, it's only been tried (or even considered) with a planet, but it theoretically could work with a star as well. As noted, the stars move along at a pretty good clip, rotating around the galactic center. Our sun's speed has been calculated at what I write in the story. Now, in the fictional universe of my tale the idea is simply to gain speed, the direction doesn't matter. The ship has to be moving very rapidly indeed in order to pass completely into the wormhole before the very short-lived hole collapses, but the direction of the movement isn't relevant.
By the way, the wormhole is also real science, though only in theory. The theory of general relativity allows for their existence as an exclusion from the normal space-time continuum. Originally such a deviation was termed an Einstein-Rosen bridge, but the more popularly used nomenclature today is Lorenzian wormhole. Needless to say, no wormhole has ever been physically observed, but the math says they're out there or at least could be.