  Bus bunching is a perennial phenomenon that not only diminishes the
efficiency of a bus system, but also prevents transit authorities from keeping
buses on schedule. We present a physical theory of buses serving a loop of bus
stops as a ring of coupled self-oscillators, analogous to the Kuramoto model.
Sustained bunching is a repercussion of the process of phase synchronisation
whereby the phases of the oscillators are locked to each other. This emerges
when demand exceeds a critical threshold. Buses also bunch at low demand,
albeit temporarily, due to frequency detuning arising from different human
drivers' distinct natural speeds. We calculate the critical transition when
\emph{complete phase locking} (full synchronisation) occurs for the bus system,
and posit the critical transition to \emph{completely no phase locking} (zero
synchronisation). The intermediate regime is the phase where clusters of
partially phase locked buses exist. Intriguingly, these theoretical results are
in close correspondence to real buses in a university's shuttle bus system.
