Quantification of the DNA damage induced by chemotherapy in patient cells may aid in personalization of the dose used. However, assays to evaluate individual patient response to chemotherapy are not available today. Here, we present an assay that quantifies single-stranded lesions caused by the chemotherapeutic drug Bleomycin (BLM) in peripheral blood mononuclear cells (PBMCs) isolated from healthy individuals. We use base excision repair (BER) enzymes to process the DNA damage induced by BLM and then extend the processed sites with fluorescent nucleotides using a DNA polymerase. The fluorescent patches are quantified on single DNA molecules using fluorescence microscopy. Using the assay, we observe a significant variation in the in vitro induced BLM damage and its repair for different individuals. Treatment of the cells with the BER inhibitor CRT0044876 leads to a lower level of repair of BLM-induced damage, indicating the ability of the assay to detect a compromised DNA repair in patients. Overall, the data suggest that our assay could be used to sensitively detect the variation in BLM-induced DNA damage and repair in patients and can potentially be able to aid in personalizing patient doses.