We present an analysis of the morphology and profiles of the dust continuum emission in 153 bright sub-millimetre galaxies (SMGs) detected with ALMA at S/N ratios of $>8$ in high-resolution $0.18''$ ($\sim1$kpc) 870$\mu$m maps. We measure sizes, shapes and light profiles for the rest-frame far-infrared emission from these luminous star-forming systems and derive a median effective radius ($R_e$) of $0.10''\pm0.04''$ for our sample with a median flux of $S_{870}=5.6\pm0.2$mJy. We find that the apparent axial ratio ($b/a$) distribution of the SMGs peaks at $b/a\sim0.63\pm0.24$ and is best described by triaxial morphologies, while their emission profiles are best fit by a Sersic model with $n\simeq1.0\pm0.1$, similar to exponential discs. This combination of triaxiality and $n\sim1$ Sersic index are characteristic of bars and we suggest that the bulk of the 870$\mu$m dust continuum emission in the central $\sim2$kpc of these galaxies arises from bar-like structures. By stacking our 870$\mu$m maps we recover faint extended dust continuum emission on $\sim4$kpc scales which contributes $13\pm1$% of the total 870$\mu$m emission. The scale of this extended emission is similar to that seen for the molecular gas and rest-frame optical light in these systems, suggesting that it represents an extended dust and gas disc at radii larger than the more active bar component. Including this component in our estimated size of the sources we derive a typical effective radius of $\simeq0.15''\pm0.05''$ or $1.2\pm0.4$kpc. Our results suggest that kpc-scale bars are ubiquitous features of high star-formation rate systems at $z\gg1$, while these systems also contain fainter and more extended gas and stellar envelopes. We suggest that these features, seen some $10-12$Gyrs ago, represent the formation phase of the earliest galactic-scale components: stellar bulges.