[KrisKrinkle]

"They are perfectly within their rights to search bags of people who leave their premises."

The following part of the Fourth Amendment needs to be emphasized:

“The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures…”

It’s important that this is a Constitutional protection from Government but for this discussion that importance is secondary to the importance that it is also an authoritative and clear statement that the right exists.

Where is it stated with equal authority (and clarity) that "They" have a right to search bags of people who leave their premises."

[Real Cynic No More]

The key is the word "unreasonable". It does not state "absolute". Again, you would be leaving their property, maybe with some of their property. If you know their rules, then to me their searching your bags could be construed as "reasonable". If you don't think it's reasonable for your bags to be searched, be reasonable by exercising your rights to shop someplace else.