Hello XXXXXXXX,
Yes. Since you are on private property, a private property owner has the right to regulate activities on its premises, including the searching of bags for possible stolen items. You may be thinking of the Fourth Amendment ban on unreasonable search and seizures. However, the Fourth Amendment only applies to government action. Since Walmart is not a part of the government (at least not yet ) it has the right to look through your bags. It is intrusive and annoying, but they do have the legal right to do it. If you do not like the practice, you obviously have the right to let Walmart know of your concerns and take your business somewhere else.
Thomas
Lawyer
Seventeen years experience as New York, New Jersey lawyer, and publisher of online legal newspaper