The thread title asks the question, “What would you do?” I would do absolutely nothing. To start with it is a cheap bike that is not worth the possibility of getting yourself in trouble over. How do you know that the bike is not a bait bike that the police are watching? It is probably not but what if it is? If it is not a bait bike there is still the possibility of being charged with being in possession of stolen property.
If the thought of it being there was driving me crazy then I would go into the store and talk to the store manager. Once the store manager is made aware that an abandoned bike is in “his” bike rack, the bike is his problem not yours.
Trust me, when I tell you the smartest thing you can do is leave this bike alone.