Is it possible to pass a (voltage-based/amplitude modulated) digital data signal using just one wire?
In virtually every situation where a signal is sent by wire, it uses (at least) two wires - one for some kind of reference voltage, and (at least) one for the data. The signal is amplitude moderated - the difference between the signal wire(s) and reference wire voltages being above, below or between certain voltages

Well .. sort of. This model breaks down for fast signals over long wires where transmission line behavior takes over. It also doesn't cover the popular 4-20ma current loop signalling system, and things like Ethernet which is isolated by tiny transformers and the ends can float as much as 1500V apart without being out of spec.
There is also radio transmission, which uses electromagnetic field coupling to transfer a signal using zero wires!

But potential takes time to build, and time to dissipate. It's not ideal and square

I think you're heading in the right direction here.
May I present: the Goubau line! This is effectively a radio wave, but the presence of the wire anchors it in space around the wire. Current doesn't actually flow in the wire.
Any form of sharp transient signal that drives a single wire will travel along the wire, behaving like a transmission line with the self-inductance of the wire and its capacitance to ground (even though that may be far away). The signal will tend to bleed off the wire, and may be reflected from the far end. The limit case of a single wire driven by an alternating signal is the classic radio aerial such as you might find on your car.
Some more general ideas are presented here.