It completely depends on their job onboard. Cruise STAFF and officers get visitor privileges that CREWMEMBERS do not get. It is very imprtant to understand the difference.
If your gal is a bartender, waitress, spa worker or shop-worker she probably does NOT have any special rates for you and you cannot stay in her cabin. It is different for staff and officers.
However - keep in mind they don't just tell them "heck, anyone you want to bring onboard anytime." They limit their chances to a one or two every year. And whther it is free or s discount. once again, depends on their jobs, and where they live.
An officer living alone on the bridge deck can have a guest, but a crewmember sharing a cabin on crew deck cannot. But she probably CAN arrange a discount for you, but you would have to say you are family or engaged, or whatever.
If she is just saying "come and see me" but she wants you to pay full fare, she may or may not be serious, it is hard to say. She may be lonely or maybe just trying to be "nice," never expecting you to really do it.
It is up to you to determine her intent, we can't help you there.