I don't think she would have had any suitors. After all, the age of 16 was when the Grand Duchesses' became "women", so that was probably the age they were allowed to marry at. (Correct me if I'm wrong) Anastasia's family fell out of power when she was 15 - not even 16. So she had no chance to even discuss the topic of marriage with her parents.
Well, I don't think 16 was the age they were allowed to marry. Remember, Nicolas rebuffed a marriage proposal for Maria when she was 16, saying that she was just a schoolgirl.
About the suitors - well, even if Anastasia had crush, she couldn't have had a
real suitor, since she died at the age of 17. She was just too young...