  Long-term studies of binary millisecond pulsars (MSPs) provide precise tests
of strong-field gravity and can be used to measure neutron-star masses.
PSR~J1909$-$3744, a binary MSP has been the subject of several pulsar timing
analyses. The edge-on orbit enables measurement of its mass using the Shapiro
delay; however, there is degeneracy in the sense of the inclination angle, $i$,
and multiple solutions for the longitude of ascending node, $\Omega$. Radio
pulsars scintillate due to inhomogeneities in the ionized interstellar medium
(IISM). This can result in scintillation arcs in the power spectrum of the
dynamic spectrum that can use these to study the interstellar medium and
constrain binary pulsar orbits. Here, we study the scintillation of
PSR~J1909-3744 using observations from the 64-m Parkes Radio Telescope
(Murriyang) over $\approx$13\, years, using techniques to study scintillation
in a lower signal-to-noise regime. By monitoring annual and orbital variations
of the arc-curvature measurements we are able to characterise the velocity of
the IISM. We find that the statistics of the IISM remained stationary over this
time and a slightly anisotropic model (axial ratio $\gtrsim1.2$) is preferred.
We measure the relative distance to a single dominant thin scattering screen at
$s=0.49\pm0.04$, or $D_s=590\pm50$\,pc, with an angle of anisotropy
$\zeta=85\pm6^\circ$ (East of North) and velocity in the direction of
anisotropy $V_{\textrm{IISM}, \zeta}=14\pm10$\,km\,s$^{-1}$. By combining a
physical model of the IISM and current pulsar timing results, we also constrain
$\Omega=225\pm3^\circ$ and $i=86.46\pm0.05^\circ$.
