I just received a postcard confirming my "free" magazine order too.
But it doesn't look like a bill, just an acknowledgement that the order will start soon (although it is weird they list a price).
Well, if a bill does arrive it's going in the garbage. If nothing else, I will get a few copies until they cut me off for non-payment.
I did keep a copy of the Barnes & Noble order screen and it clearly says:
"We hope you enjoy your free subscription for XXXXXXXXXXX. Please allow 4-10 weeks for delivery. This is standard publishing industry lead-time. Please contact us at [email protected]
if you have any questions about your subscription, and reference order number XXXXXXX."
Notice the phrase "free subscription".