We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies ($0.15< z<0.65$) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle $\theta$, of the galaxy density contrast $\delta _{\rm g}$ and the weak lensing convergence $\kappa$, in the vicinity of these identified troughs and peaks, referred to as 'void' and 'cluster' superstructures. The ratio of the profiles depend mildly on $\theta$, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta)$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta)$ using a suite of N-body (Gower Street) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fitting Planck cosmology. Similar values with $\sim 0.1\sigma$ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 $3\times 2$-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.