Constrained peptides are emerging as promising structures in therapeutic development. Offering compatibility with genetically encoded libraries for drug discovery, biocompatible methods to constrain peptides are particularly attractive. While there are many such methods to construct cyclic and stapled peptides, the biocompatible generation of bicyclic peptides is less explored. Addressing this need for biocompatible and selective ways to generate peptide bicycles, we previously developed a strategy based on noncanonical amino acids leveraging the reactivity of cyanopyridine and 1,2-aminothiol. This protocol provides detailed step-by-step instructions for the synthesis of these peptide bicycles and is designed to be accessible even to laboratories with limited synthetic chemistry resources. It outlines the solid-phase peptide synthesis of linear peptide precursors that efficiently form bicyclic structures in aqueous buffer at physiological pH. Utilizing commercially available building blocks, we devised a method to synthesize the noncanonical amino acids that are essential for bicyclization directly on the solid support during peptide synthesis.