I never gave a thought to putting my bag there until I saw on tv (Oprah comes to mind, maybe it was on her show years ago), where people were given swabs, told to test places as they went about their day, and label them. Then they were sent off and analyzed. The kid seat and handle of shopping trollies were both near the very top for contamination, including fecal.
Nowdays I grab one of the sanitizing wipes the shop provides, wipe the handle before moving the trolly and keep my bag on my shoulder.