  We confirm the presence of a mean-field Bose glass in 2D quasicrystalline
Bose-Hubbard models. We focus on two models where the aperiodic component is
present in different parts of the problem. First, we consider a 2D
generalisation of the Aubry-Andr\'e model, where the lattice geometry is that
of a square with a quasiperiodic onsite potential. Second, we consider the
randomly disordered vertex model, which takes aperiodic tilings with
non-crystalline rotational symmetries, and forms lattices from the vertices and
lengths of the tiles. For the disordered vertex models, the mean-field Bose
glass forms across large ranges of the chemical potential, and we observe no
significant differences from the case of a square lattice with uniform random
disorder. Small variations in the critical points in the presence of random
disorder between quasicrystalline and crystalline lattice geometries can be
accounted for by the varying coordination number and the different rotational
symmetries present. In the 2D Aubry-Andr\'e model, substantial differences are
observed from the usual phase diagrams of crystalline disordered systems. We
show that weak modulation lines can be predicted from the underlying potential
and may stabilise or suppress the mean-field Bose glass in certain regimes.
This results in a lobe-like structure for the mean-field Bose glass in the 2D
Aubry-Andr\'e model, which is significantly different from the case of random
disorder. Together, the two quasicrystalline models studied in this work show
that the mean-field Bose glass phase is present, as expected for 2D
quasiperiodic models. However, a quasicrystalline geometry is not sufficient to
result in differences from crystalline realisations of the Bose glass, whereas
a quasiperiodic form of disorder can result in different physics, as we observe
in the 2D Aubry-Andr\'e model.
