According to Stephenie Meyer, Bella does get her period, but this type of blood is "dead blood," and even though it does bother Edward a bit (considering he's a vampire and all), he's too much of a gentleman to comment about it.
when Bella has her period and yes it does bother edward a bit but the blood from her period isn't fresh blood or "dead blood" not like a fresh cut. anyway edward is too much of a gentleman to say...