The most appropriate next step in management is to switch the intravenous proton pump inhibitor (PPI) to an oral PPI because this patient's low-risk ulcer does not require prolonged intravenous treatment or observation. Low-risk gastric ulcers are clean-based or have a nonprotuberant pigmented spot and should be treated with oral PPI therapy, initiation of refeeding within 24 hours, and early hospital discharge.

Blood transfusion should be performed in patients with (1) hemodynamic instability and ongoing bleeding or susceptibility to complications from oxygen deprivation (for example, ischemic heart disease) and (2) a hemoglobin level less than 7 g/dL (70 g/L) if hemodynamically stable with no active or massive bleeding. This patient does not meet these criteria.

Endoscopic treatment of the ulcer is not appropriate because clean-based ulcers are at low risk for rebleeding and the risks of endoscopic therapy outweigh any potential benefits in this patient.

Octreotide is not a routine treatment, even for acute active bleeding, unless variceal bleeding is suspected. This patient has a low-risk ulcer and no evidence of esophageal varices, so octreotide is not indicated.