I am not positive, but...
If there are written notices specifically stating that is their policy, you have the option not to shop there, but they do have the option to search your bag.

In most cases you are correct, but I know that my local target store has thee notices and they do search bags. So does Costco and some retailers at the mall.

I found a Link

Well, it is private property, and they can do that. But they aren't law enforcement. When the cops search you on the bus or train for no reason in DC, they are doing it for security and are looking for explosives. But if they find drugs, you are going to jail for that. If a security guy looks in your bag as you are leaving a store and sees a baggie of weed, I don't think he has the authority to detain you for that.

Good question, but I bet he could call the cops and take down your plate number.

Did you read your link?
Bag searches are only legal if they're voluntary (says so in your link repeatedly). When they stop you to check your receipt at Walmart, you can simply say "no". Trust me, I've done it several times. If you let them, they are only going to look at the bags of merchandise you just bought and check it against your receipt - they are not going to look in your purse or backpack.

Certainly pubs and clubs here will call the police if they find you with drugs on your person.

Yes I did read the link. I know what it says - I was sharing both personal experience and then a link differentiating the two.

Inasmuch as there hasn't been any -- I'd've known -- maybe you're right.

For years there has been a deal of bellowing about "Our rights are violated, including our rights under the Third Amendment, and others ad nauseam! And you're all oppressed!" from people who are driven less by civil rights concerns than by the most virulent and discreditable prejudice against Republicans. These bellowers are without credibility, being penile-encephaly cases all. Their allegations just don't impress the thoughtful as having any substance. You'd think these fellows don't want to win the war or something, the way they violently objected to every imaginable measure to actually win it.

*blinks*

Yes, Dana, it's something you don't really know much about, but among our 300 millions we've got some of these jackanapes too. They don't strike me as altogether rational.

I'm sure if they could find you, they'd be glad to strike you.

Being less than rational. But I know how to cause an irruption of rationality into such people.

In this case, the officials behind the policy are mostly Democrats.

That's because of your increase in video surveillance, most likely.

They did overwhelmingly approve Patriot Act 2 and all the further laws which allowed unwarrantless wiretapping.

...or something kinda like that...