In this paper, a proof-of-concept study of a $1$-bit wideband reconfigurable intelligent surface (RIS) comprising planar tightly coupled dipoles (PTCD) is presented. The developed RIS operates at subTHz frequencies and a $3$-dB gain bandwidth of $27.4\%$ with the center frequency at $102$ GHz is shown to be obtainable via full-wave electromagnetic simulations. The binary phase shift offered by each RIS unit element is enabled by changing the polarization of the reflected wave by $180^\circ$. The proposed PTCD-based RIS has a planar configuration with one dielectric layer bonded to a ground plane, and hence, it can be fabricated by using cost-effective printed circuit board (PCB) technology. We analytically calculate the response of the entire designed RIS and showcase that a good agreement between that result and equivalent full-wave simulations is obtained. To efficiently compute the $1$-bit RIS response for different pointing directions, thus, designing a directive beam codebook, we devise a fast approximate beamforming optimization approach, which is compared with time-consuming full-wave simulations. Finally, to prove our concept, we present several passive prototypes with frozen beams for the proposed $1$-bit wideband RIS.