An accurate force field (FF) is the foundation of reliable results from molecular dynamics (MD) simulations. In our recently published work, we developed a protocol to generate atom pair-specific Lennard-Jones (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) parameters in the context of the Drude polarizable FF based on readily accessible quantum mechanical (QM) data to fit condensed phase experimental thermodynamic benchmarks, including the osmotic pressure, diffusion coefficient, ionic conductivity, and solvation free energy, when available. In the present work, the developed protocol is applied to generate NBFIX and NBTHOLE parameters for interactions between monatomic ions (specifically Li+, Na+, K+, Rb+, Cs+, and Cl-) and common functional groups found in proteins and nucleic acids. The parameters generated for each ion-functional group pair were then applied to the corresponding functional groups within proteins or nucleic acids followed by MD simulations to analyze the distribution of ions around these biomolecules. The modified FF successfully addresses the issue of overbinding observed in a previous iteration of the Drude FF. Quantitatively, the model accurately reproduces the effective charge of proteins and demonstrates a level of charge neutralization for a double-helix B-DNA in good agreement with the counterion condensation theory. Additionally, simulations involving ion competition correlate well with experimental results, following the trend Li+ > Na+ ≈ K+ > Rb+. These results validate the refined model for group 1 ion-biomolecule interactions that will facilitate the application of the polarizable Drude FF in systems in which group 1 ions play an important role.