Aortic stenosis with anticoagulant use: This is the most likely diagnosis given the combination of aortic stenosis and bleeding, as anticoagulants are commonly used in patients with aortic stenosis to prevent thromboembolic events, and their use can increase the risk of bleeding.

Gastrointestinal bleeding due to angiodysplasia: Patients with aortic stenosis are at increased risk of gastrointestinal bleeding due to angiodysplasia, which are vascular malformations in the gut that can bleed easily.
Bleeding due to antiplatelet therapy: Patients with aortic stenosis may also be on antiplatelet therapy, which can increase the risk of bleeding.
Heyde's syndrome: This is a condition characterized by aortic stenosis, gastrointestinal bleeding, and angiodysplasia, and is thought to be due to the shear stress caused by the aortic stenosis leading to the formation of angiodysplasias.

Aortic dissection: Although less likely, aortic dissection is a life-threatening condition that can cause bleeding and must be considered in the differential diagnosis of a patient with aortic stenosis and bleeding.
Pulmonary embolism: Patients with aortic stenosis are at increased risk of pulmonary embolism, which can cause bleeding and must be considered in the differential diagnosis.

Hemophilia: Although rare, hemophilia can cause bleeding and must be considered in the differential diagnosis of a patient with aortic stenosis and bleeding, especially if there is a family history of bleeding disorders.
Vasculitis: Certain types of vasculitis, such as giant cell arteritis, can cause aortic stenosis and bleeding, and must be considered in the differential diagnosis.
Bleeding due to cancer: Certain types of cancer, such as gastrointestinal cancer, can cause bleeding and must be considered in the differential diagnosis of a patient with aortic stenosis and bleeding.