In the last two decades, a tremendous amount of attention has been directed towards the design of antibacterial silver(I)-based materials, including coordination polymers (CPs) built up with a great variety of oxygen and nitrogen-containing ligands. Herein, a family of six new silver(I)-based CPs, having the general stoechiometric formula [Ag(H2DMPMB)(X)] (X = NO3, 1; CF3CO2, 2; CF3SO3, 3; BF4, 4; ClO4, 5; and PF6, 6) and incorporating the flexible ditopic pyrazolyl-type ligand 4,4′-bis((3,5-dimethyl-1H-pyrazol-4-yl)methyl)biphenyl (H2DMPMB), has been prepared by the chemical precipitation method involving the reaction of silver(I) salts with H2DMPMB in the 1:1 molar ratio, in alcohols, or acetonitrile at room temperature for two-hours. The new silver(I)-based polymeric materials were characterized by means of Fourier transform infrared spectroscopy (FTIR), elemental analysis (EA), and thermogravimetric analysis (TGA), allowing for the proposition that their structures comprise one-dimensional chains, with the silver(I) ions mostly assuming a T-shapped stereochemistry completed by the exo-bidentate ligands and counter-anions. The obtained silver(I) CPs showed a remarkable light insensitivity and stability in the air, are insoluble in water and in most common organic solvents, and possess appreciable thermal stabilities spanning the range 250–350 °C. The antibacterial activity of the obtained silver(I) CPs was tested against the Gram-negative bacteria Escherichia coli (E. coli) and Gram-positive bacteria Staphylococcus aureus (S. aureus) using the Tetrazolium/Formazan test (TTC), by measuring the bacterial viability at different time intervals. The complete reduction of both bacterial strains occurred after 24 h of exposure to all silver(I) CPs, the bacterial viability values for S. aureus reaching 8% for compounds 3, 5, and 6 after only two-hours.