  Context. Observational evidence has accumulated in the past years, showing
that the Galactic bulge includes two populations, a metal poor and a metal rich
one that, in addition to a different metallicity, show different alpha over
iron abundances, spatial distribution, and kinematics. While the metal rich,
barred component has been fairly well characterized, the metal poor, spheroidal
component has been more elusive and harder to describe. RR Lyrae variables are
clean tracers of the old bulge component, and they are, on average, more metal
poor than red clump stars.
  Aims. In the present paper, we provide a new catalog of 16488 ab type RR
Lyrae variables in the bulge region within -10<l<10 and -2.8<b<2.8, extracted
from multi epoch PSF photometry performed on VISTA Variable in the Via Lactea
survey data. We used the catalog to constrain the shape of the old, metal poor,
bulge stellar population.
  Methods. The identification of ab type RR Lyrae among a large sample of
candidate variables of different types has been performed via a combination of
a Random Forest classifier and visual inspection... [abridged]
  Results. We use the present catalog to derive the shape of their distribution
around the Galactic Center, resulting in an elongated spheroid with projected
axis ratio b/a~0.7 and inclination angle ~20 degrees. We discuss how
observational biases such as errors on the distances and a non-uniform sampling
in longitude, affect both the present measurements and previous ones,
especially those based on red clump stars... [abridged]
  Conclusions. We publish a high purity RRab sample for future studies of the
oldest Galactic bulge population, close to the midplane. We explore different
choices for the period-luminosity-metallicity relation, highlighting how some
of them introduce spurious trends of distances with either period or
metallicity, or both... [abridged]
