Blue roses exist in fantasy but not in nature. The blue rose symbolizes the unattainable or impossible which won't make it a good choice to give someone you would like to maintain a relationship with anyway.
The quest for a blue rose continues, since they are merely a fabrication of the eager, dreaming mind at this point. The blue roses that exist are actually variations of purple or lavender, which look blue in certain light. However, you wouldn't really want to send a blue rose to someone, as it means a figment of the imagination, or something unobtainable. If you like blue roses just because they are different, consider the decadent Blue Moon hybrid tea rose.