The difference in arc length is
W*theta
where W is the offset (the width of the car), and theta is the angle you turned through in radians. If you are going around a 90-degree turn and stay (1+W) feet from the curb the whole time, then the formula works with theta replaced by pi/2. But for less turn you'd have to estimate theta, and I would be concerned about people, including myself, trying to do that.
BTW, the formula works whether the curvature of the turn is constant or not. The difference between adjacent lanes on a track is 2*pi*W, where W is the width of the lane, even if the turns are not a constant curvature, i.e., circular.
Instead, what I do when faced with this situation is to hop up on the curb and walk my bike past the car on the inside. It's usually much less than 90 degrees, so it's less than a foot shorter than following the true SPR since the W in that case is about 1 foot.