Should I give her a rose and card?

Well that depends on what you would prefer or what is more convenient. What is important is what you say in the card. Don't come on too strong since she just got out of a relationship that didn't work, but let her know how you feel and that you like her and like spending time with her. Throw in a compliment or two but don't over do it. Tell her that you would like to stay in touch and hang out sometime etc. Basically just anything you really want to say to her. Good Luck. Hope things work out!