  We use numerical simulations to model Gaia DR3 data with the aim of
constraining the Milky Way bar and spiral structure parameters. We show that
both the morphology and the velocity field in Milky Way-like galactic disc
models are strong functions of time, changing dramatically over a few tens of
Myr. This suggests that by finding a good match to the observed radial velocity
field, v_R(x,y), we can constrain the bar-spiral orientation. Incorporating
uncertainties into our models is necessary to match the data; most importantly,
a heliocentric distance uncertainty above 10-15% distorts the bar's shape and
v_R quadrupole pattern morphology, and decreases its apparent angle with
respect to the Sun-Galactocentric line. An excellent match to the Gaia DR3
v_R(x,y) field is found for a simulation with a bar length R_b\approx3.6 kpc.
We argue that the data are consistent with a MW bar as short as ~3 kpc, for
moderate strength inner disc spiral structure (A_2/A_0\approx0.25) or,
alternatively, with a bar length up to ~5.2 kpc, provided that spiral arms are
quite weak (A_2/A_0\approx0.1), and is most likely in the process of
disconnecting from a spiral arm. We demonstrate that the bar angle and distance
uncertainty can similarly affect the match between our models and the data - a
smaller bar angle (20 deg instead of 30 deg) requires smaller distance
uncertainty (20% instead of 30%) to explain the observations. Fourier
components of the face-on density distribution of our models suggest that the
MW does not have strong m=1 and/or m=3 spirals near the solar radius.
