Bleeding is the most feared complication of anticoagulation. We sought to investigate whether the bleeding risk acceptance has a prognostic value during long-term follow-up in the era of direct oral anticoagulants (DOACs) among patients with atrial fibrillation (AF). We studied 167 consecutive AF outpatients [aged 68.8 SD 10.6 years; 141 (84.4%) on DOACs]. The bleeding acceptance was assessed based on the Bleeding Ratio defined as the declared maximum number of major bleedings that a patient would be willing to accept to prevent one major stroke. We recorded cerebrovascular ischemic events, major or clinically relevant non-major bleeds (CRNMB), and mortality. A median Bleeding Ratio was 4 (IQR 2–5). During follow-up of 946 patient-years, cerebrovascular ischemic events and/or death were observed in 28 patients (3.3%/ year) and major bleeding or CRNMB in 33 (4.6%/ year). The Bleeding Ratio was lower in patients who experienced cerebrovascular events or death (p = 0.004), but not bleeding. Patients with the Bleeding Ratio 0–3 were more often non-persistent to the OAC therapy, and more likely to have cerebrovascular event or die than those with higher bleeding acceptance (odds ratio 2.55; 0.95% CI 1.08–6.02) which was driven by the impact on mortality. The multiple Cox proportional hazards model showed that lower Bleeding Ratio, higher CHA2DS2-VASc score, and older age predicted cerebrovascular events or death during follow-up. AF patients who are willing to accept fewer serious bleedings to avoid major stroke during anticoagulation are more likely to experience death and/or cerebrovascular ischemic events, but not bleeding, what might be related to non-persistence.