If I've managed to finally understand what the gist of Bernstein and Phillips article is about, here's what I think it is. The geometry of the gauge field (read: field of phase changes) concerned looks like a truncated cone capped with a spherical dome. That means, there is a hemisphere which has a line of latitude extended to a surface with constant curvature. So the bundle of fibers from that circle of latitude and lying over the conical surface (a section of the total space), has planes 'stacked' along each fiber at a constant angle, each electron sees a 'wide' ramp it transports the direction of its phase angle around, in the connection. The curvature of the connection corresponds (topologically) to the solenoid field in the A-B experiment, and the shift in phase corresponds to the angular excess of a geodesic around the truncated cone (this unrolls to a straight line in the plane, and all the phase vectors are parallel there). So what that actually says about what a gauge field is in terms of electrons interacting with a field potential, I still can't say in so many words. But the electrons encounter a spacetime which is curved by the presence of a potential, the electromagnet is shielded and there is no magnetic field (?). Another clue there is that the spherical part of the curved space corresponds to that part of the spacetime that does contain a magnetic field (i.e. is inside the shield).