The merger of binary neutron star (BNS) systems are predicted to be progenitors of short gamma-ray bursts (GRBs); the definitive probe of this association came with the recent detection of gravitational waves (GWs) from a BNS merger by Advanced LIGO and Advanced Virgo (GW170817), in coincidence with the short GRB 170817A observed by Fermi-GBM and INTEGRAL. Short GRBs are also expected to emit very-high energy (VHE, > 10S0 GeV) photons and VHE electromagnetic (EM) upper limits have been set with observations performed by ground-based gamma-ray detectors and during the intense EM follow-up campaign associated with GW170817/GRB 170817A. In the next years, the searches for VHE EM counterparts will become more effective thanks to the Cherenkov Telescope Array (CTA): this instrument will be fundamental for the EM follow-up of transient GW events at VHE, owing to its unprecedented sensitivity, rapid response (few tens of seconds) and capability to monitor large sky areas via survey-mode operation. We present a comprehensive study on the prospects for joint GW and VHE EM observations of merging BNSs with Advanced LIGO, Advanced Virgo and CTA, based on detailed simulations of the multi-messenger emission and detection. We propose a new observational strategy optimized on the prior assumptions about the EM emission. The method can be further generalized to include other electromagnetic emission models. According to this study CTA will cover most of the region of the GW skymap for the intermediate and most energetic on-axis GRBs associated to the GW event. We estimate the expected joint GW and VHE EM detection rates and we found this rate goes from 0.08 up to 0.5 events per year for the most energetic EM sources.