Although it may seem old-fashioned, I'd like to suggest making a tape instead of a CD for her. Making tapes requires more attention to the detail, for the example the arrangements of tracks or the lenght of the pauses and you will have to sit until one track ends, put in another song to record and so on. It's got that special touch to it because the receiving person knows how much effort will have gone into that tape. Of course, Cds are more user-friendly and you will have more flexibility. And if you are really into it, a CD can be made very special, too, such as mixing the songs together or creating a nice cover. In any case, since tapes are more special, misunderstandings can occur unless both parties are very clear about the motivations. Making tapes for friends is a very cool thing in my opinion although it's probably more fun when the unknown is part of the equation as well. Anyway, it's just a thought.
Regarding the romantic songs, which genre does your lady-friend prefer? The age may also play a role. And is she more into jazz, classical, pop, hiphop/rnb, rock, others or a mixture of genres? Do you prefer acoustic or vocal songs? Would you like to use popular tracks or something more unknown?
Further, since English is not my first language, I don't know what connotations "lady-friend" has. This might influence the choice of either male or female vocals and the appropriate lyrics.
Just a few songs out of my head (contemporary, melodic, vocal, female jazz, rather easy to listen to):
Silje Nergaard – Waltz
Lisa Nilsson - Those Who Were
Beady Belle - September
Leni Stern - Bury me Standing (very romantic although not necessarily implied in the title)