The RaPID (random non-standard Peptides Integrated Discovery) system is a powerful methodology for the identification of bioactive cyclic and bicyclic peptides, and has been previously used to great effect to find both inhibitors and agonists of a wide range of protein targets. However, peptides in general as well as those discovered by the RaPID system often suffer from poor permeability across biological membranes, diminishing their utility for intracellular targeting. We reasoned that cyclic peptides containing two non-canonical long aliphatic side chains may be able to adopt both hydrophobic (i.e. side chains outwards) and hydrophilic (i.e. side chains inwards forming a virtual bicyclic structure) conformations, thus facilitating membrane permeability. Using genetic reprogramming combined with mRNA display, we screened a library of greater than 1013 such bicyclic peptides for binding to the human histone-modifying enzyme peptidyl arginine deiminase 4 (PAD4). In this manner, two virtual bicyclic peptides were identified, which exhibited very strong binding affinities for, and moderately strong inhibitory activities against, PAD4. Moreover, one of these peptides exhibited membrane permeability in cell culture studies, demonstrating the utility of this scaffold for the isolation of membrane permeable inhibitors of target proteins.