Semiconductor ring lasers are semiconductor lasers where the laser cavity consists of a ring-shaped waveguide. SRLs are highly integrable and scalable, making them ideal candidates for key components in photonic integrated circuits. SRLs can generate light in two counterpropagating directions between which bistability has been demonstrated. Hence, information can be coded into the emission direction. This bistable operation allows SRLs to be used in systems for all-optical switching and as all-optical memories. For the demonstration of fast optical flip-flop operation, Hill et al. [Nature 432, 206 (2004)] fabricated two SRLs coupled by a single waveguide, rather than a solitary SRL. Nevertheless, the literature shows that a single SRL can also function perfectly as an all-optical memory. In our recent paper [W. Coomans et al., Phys. Rev. A 88, 033813, (2013)], we have raised the question whether coupling two SRLs to realize a single optical memory has any advantage over using a solitary SRL, taking into account the obvious disadvantage of a doubled footprint and power consumption. To provide the answer, we have presented in that paper a numerical study of the dynamical behavior of semiconductor ring lasers coupled by a single bus waveguide, both when weakly coupled and when strongly coupled. We have provided a detailed analysis of the multistable landscape in the coupled system, analyzed the stability of all solutions and related the internal dynamics in the individual lasers to the field effectively measured at the output of the waveguide. We have shown which coupling phases generally promote instabilities and therefore need to be avoided in the design. Regarding all-optical memory operation, we have demonstrated that there is no real advantage for bistable memory operation compared to using a solitary SRL. An increased power suppression ratio has been found to be mainly due to the destructive interference of the SRL fields at the low power port. Also, multistability between several modal configurations has been shown to remain unavoidable.