The rise of drug-resistant influenza A virus strains motivates the development of new antiviral drugs, with different structural motifs and substitution. Recently, we explored the use of a bicyclic (bicyclo[3.1.0]hexane) analogue of sialic acid that was designed to mimic the conformation adopted during enzymatic cleavage within the neuraminidase (NA; sialidase) active site. Given that our first series of compounds were at least four orders of magnitude less active than available drugs, we hypothesized that the new carbon skeleton did not elicit the same interactions as the cyclohexene frameworks used previously. Herein, we tried to address this critical point with the aid of molecular modeling and we proposed new structures with different functionalization, such as the introduction of free ammonium and guanidinium groups and ether side chains other than the 3-pentyl side chain, the characteristic side chain in Oseltamivir. A highly simplified synthetic route was developed, starting from the cyclopropanation of cyclopentenone and followed by an aziridination and further functionalization of the five-member ring. This allowed the efficient preparation of a small library of new bicyclic ligands that were characterized by enzyme inhibition assays against influenza A neuraminidases N1, its H274Y mutant, and N2. The results show that none of the new structural variants synthesized, including those containing guanidinium groups rather than free ammonium ions, displayed activity against influenza A neuraminidases at concentrations less than 2 mM. We conclude that the choice and positioning of functional groups on the bicyclo[3.1.0]hexyl system still need to be properly tuned for producing complementary interactions within the catalytic site.