"A tunnel of bent space stretching in front of the ship" sounds cool but isn't consistent with how it's done in Trek.
Arguably, it's pretty much how it was done in TMP.
And indeed if one wouldn't need to stretch space all the way from A to B into a wormhole, and an extension of X ly would do the trick, why shouldn't an extension of two millimeters be fine as well?
Probably because contracting the space around your ship by two millimeters would result in a relative motion of two millimeters per second. By the same token, your starship could be rendered entirely weightless in Earth gravity by creating a distortion field that "lengthens" space by exactly 9.8 meters along the ship's dorsal axis.
The same field, stretched two hundred billion kilometers ahead of the ship, would cause the ship to accelerate forward at two hundred billion kilometers per second.