Respiratory infectious diseases have challenged medical communities and researchers. Ceftriaxone, meropenem and levofloxacin are widely used for bacterial infection treatment, although they possess severe side effects. To overcome this, we propose cyclodextrin (CD) and CD-based polymers as a drug delivery system for the drugs under consideration. CD polymers demonstrate higher binding affinity for levofloxacin (Ka ≈ 105M) compared to drug–CD complexes. CDs slightly alter the drugs’ affinity for human serum albumin (HSA), whereas CD polymers increase the drugs’ binding affinity up to 100 times. The most significant effect was observed for more the hydrophilic drugs ceftriaxone and meropenem. The drug’s encapsulation in CD carriers leads to a decrease in the degree of change in the protein’s secondary structure. The drug–CD carrier–HSA complexes demonstrate satisfying antibacterial activity in vitro, and even a high binding affinity does not decrease the drug’s microbiological properties after 24 h. The proposed carriers are promising for a drug form with a prolonged drug release.