The reference to Red Riding Hood didn't bother me (now that she's not stopping by my house anymore! )
When I was a kid, girls would say "Aunt Flo" was visiting.
When my 83-year old mom was a kid, she and her sisters would send their brothers to the store for kotex (long before tampons) and the code word was "corn flakes." (She was the oldest girl of 10 children.)
Here's a fascinating site that has about a ZILLION expressions for menstruation from all over the world. Who knew there were so many?