Nothing Ardra did requires access to the Enterprise systems, and it is consistent with the rest of the series(es).
Yet all of the Federation's known enemies (including the Borg) seemed to follow the logical "penetrate/destroy shields or have them lowered" formula for forced entry. (I doubt a con-artist's starship has capability far exceeding the Federation's more famous enemies!)
They key here is "or have them lowered". The Enterprise does not have its shields up all the time, and had no reason to put them up while in orbit of a friendly planet. Ardra didn't have any shields blocking her from beaming in and out of the Enterprise.
She also manages to disable core functioning aspects of the ship (transporter, communicators etc.)
When she visits Picard in his quarters, he's unable to use the comms or the door. This is possible by way of a localized dampening field, probably generated by a device that was beamed in with her. And her depiction of Picard's "perfect woman" can be inferred by how he acts, mixed with knowledge of Earth's history (which we know she has because of the form she took during the trial).
Why didn't they detect her beaming in and out? Energy requirements. The ship is not continually scanning for everything all the time - that's why they usually bring out a tricorder when they need to detect a transporter signature. In DS9 we are treated to additional instances of this, with Sloan regularly beaming in and out of DS9 without detection.
But in this case scanning for it wouldn't likely have helped much. In DS9 6x18, Inquisition, at Sloan's first appearance, he somehow managed to hide his transporter signature - something a con artist who relies on hiding her use of technology would surely know how to do.