[IronJack]

I suspect you have the right to refuse. And I also suspect they have the right to refuse to allow you to leave the store with the bag if you do. However, it isn't like they can just keep the merchandise you paid for; they'd have to give you a refund. And they can't detain you unless they have probable cause, and I doubt that refusal to allow them to search your bag is in itself probable cause.

If you're the kind that likes confrontation, it might be worth a shot. Refuse, and see what they do when the ball is in their court.

[television is just wrong]

I don't particularly like confrontations, but I feel this is an invasion of my privacy.

And they are making an assumption I am stealing from them.