  We numerically investigate the dynamics of how a close stellar fly-by
encounter of a symmetrical circumstellar planetesimal disc can give rise to the
many kinds of asymmetries and substructures attributed to the edge-on dusty
disc of Beta Pic. In addition we present new optical coronagraphic observations
of the outer parts of Beta Pic's disc, and report that the radial extent is
significantly greater than was found in previous measurements. The
northeasterly extension of the disc's midplane is now measured out to 1835au
from the star; the southwesterly component is measured out to 1450au. Hence we
use the length asymmetry induced in a distribution of simulation test particles
as the principal diagnostic feature when modelling the disc response, in order
to constrain fly-by parameters. In particular we favour a low inclination
prograde and near-parabolic orbit perturber of mass approximately 0.5 Solar
masses. These initial conditions suggest that the perturber could have been
physically associated with Beta Pic prior to the encounter. Thus we also
consider the possibility that the perturber could be bound to Beta Pic: a
consideration also of general interest where dust discs are known to exist in
binary star systems. In some of our models, we can relate groupings of
perturbed particles to the large-scale structure of the Beta Pic disc. The
groupings correspond to: high eccentricity and inclination particles that reach
apocentre and maximum height in the southwest, moderately eccentric and low
inclination particles that reach apocentre in the northeast, and relatively
unperturbed particles inside approximately 200au radius.
