My initial reaction was similar to the frame challenge from <PERSON>.
However, this perhaps instead gives a suitable set of pseudo-science explanations for the functioning of the drive...
The number of possible reference frames are as vast as the universe itself - a reference frame in which you have constant linear velocity relative to the immediate surroundings [unless acted on by a force] is basically the physics we have now (and "the immediate surroundings" changes as you move according to that velocity).
So the drive allows you to change what reference frame you maintain constant velocity relative to e.g.:
* standing still on the surface of a planet, you engage the drive, selecting the centre of the planet on which you are standing as the reference frame. The planet continues to rotate, but no longer affected by its gravity [i.e. no longer tied to the reference frame that is constantly accelerating towards the centre of the planet] you continue travelling tangential to the surface of the planet. The effect from an observer on the planet's surface is that you slowly start to drift upwards, accelerating faster and faster until you disappear from view in the sky.
* from the same place, you instead select the centre of the solar system - as well as the effect from the planet's rotation, you now also have an effect from the planet's orbit. Your apparent acceleration (negating the effect of the planet's own acceleration towards its sun) could be in any direction relative to the planets surface, depending on time of day...
* similarly, if you select the centre of the galaxy, or a different planet or a different star etc. there'll be even more apparent acceleration for local observers. Pick a reference frame that itself is strongly accelerated, and you'll start accelerating very strongly (e.g. even within our own solar system you might consider mercury, or a comet on a close pass to the sun)
With an infinite number of reference frames to choose from, the trick would be to find one that actually accelerates you in the direction you want, and which then will also decelerate you relative to the target planet in time for when you switch the drive off, and end up conveniently in orbit around the target planet. 562
Skilled navigators could switch between multiple observer reference frames mid-flight.
There's a huge amount of hand-waving here of course, but the intention would be that an observer in your chosen reference frame would observe you continuing to move with constant linear velocity, which other observers near to you would perceive as massive acceleration in their own reference frames.
However, unnoticed by the early experiments, which used large planets or stars as the reference frame for a lightweight experimental device, there's an equal and opposite effect on the chosen reference frame. Not only is there a (potentially very large) effective force on you to allow you to be observed with constant linear velocity from your chosen reference frame, but there's an equal an opposite force on the object(s) at the chosen reference frame.
Taking the possible effects to the extreme, consider the case where either you or the chosen "observer reference frame" were near a black hole. As you (or the chosen observer) approach the event horizon, you would still need to be observed as having constant linear velocity by the observer, despite the massive disruption of spacetime in the vicinity of the black hole... and that implies enormous acceleration effects, and probably some changes in time perception, for you or the chosen observer, or possibly both.
... but beyond a certain limit, the energy transmission capacity of the drive itself just breaks. As you pass over an event horizon of a sufficiently large black hole, it's certainly possible that a relatively nearby and relatively lightweight observer could be dragged in with you in order to continue to observe you with constant linear velocity at least for a little while... or that a sufficiently massive and distant observer would "drag you away" from the black hole as you continue on what they observe as a constant linear velocity almost but not quite touching the event horizon, but the energy to do that if you use a more massive "anchor" object (and have a linear trajectory from the observer's perspective that gets too close to the event horizon) would exceed the capacity of the link itself, perhaps having a similar effect as if you'd turned the drive off prematurely; it probably doesn't end well for you in that case.
A differently-dimensioned analogy
Suppose rather than a "constant linear velocity" we instead want the observer and you to maintain a constant distance. The equivalent of this "warp drive" is a rigid rod (or a rope under tension) with you at one end and the "observer" at the other. Until you let go of the rod/rope or it breaks, you'll stay a fixed distance from the observer - any movement by either of you will only be possible if the other moves too, unless the movement happens to be such that the distance stays the same. 43