GI side effects in general and bleeding in particular are higher in analgesic dose level of aspirin. Aspirin is a very blunt instrument - it is both anti-inflammatory and anti-thrombotic - it destroys your platelet function even in low doses - this can be a feature/benefit (ie stroke and coronary artery disease or MI) - but for pure analgesia it usually just means increasing bleeding risk for no benefit.
I don't believe this is a meaningful risk for a healthy person just taking a few aspirin. Certainly you don't want to consume too much (like all medicines) nor use it chronically (unless the alternative risks are worse).
