  Constraining when and how reionisation began is pivotal for understanding
when the first galaxies formed. Lyman-alpha (Ly$\alpha$) emission from galaxies
is currently our most promising probe of these early stages. At z>7 the
majority of galaxies detected with Ly$\alpha$ are in candidate overdensities.
Here we quantify the probability of these galaxies residing in large ionised
bubbles. We create (1.6 Gpc)$^3$ reionising intergalactic medium (IGM)
simulations, providing sufficient volume to robustly measure bubble size
distributions around UV-bright galaxies and rare overdensities. We find $M_{\rm
UV} \lesssim -16$ galaxies and overdensities are $\gtrsim$10-1000x more likely
to trace ionised bubbles compared to randomly selected positions. The brightest
galaxies and strongest overdensities have bubble size distributions with
highest characteristic size and least scatter. We compare two models: gradual
reionisation driven by numerous UV-faint galaxies versus more rapid
reionisation by rarer brighter galaxies, producing larger bubbles at fixed
neutral fraction. We demonstrate that recently observed z~7 overdensities are
highly likely to trace large ionised bubbles, corroborated by their high
Ly$\alpha$ detection rates. However, the z~8.7 association of Ly$\alpha$
emitters in EGS and GN-z11, with Ly$\alpha$ at z=10.6, are unlikely to trace
large bubbles in our fiducial model -- 11% and 7% probability of >1 proper Mpc
bubbles, respectively. Ly$\alpha$ detections at such high redshifts could be
explained by: a less neutral IGM than previously expected; larger ionised
regions at fixed neutral fraction; or if intrinsic Ly$\alpha$ flux is unusually
strong in these galaxies. We discuss how to test these scenarios with JWST and
the prospects for using upcoming wide-area surveys to distinguish between
reionisation models.
