Being a weoman and having hemophilia is a very bad idea for obvious reasons.
I don't think it works that way, though. Menstrual discharge consists mostly of the lining of the uterus that has broken down, it's not blood flowing from a severed vein so they don't keep bleeding in that situation, as far as I know.
And women can have hemophilia, it just less likely. Their two X chromosomes have to carry the recessive gene to have hemophilia, whereas men only need their one X chromosome to carry the gene.
Basically, if hemophilia was not on a sex-linked gene, men and women would be equally likely to express the gene. Also, men could be non-symptomatic carriers as well as women, since their other chromosome pairs could have 1 hemophilia gene and 1 normal gene which would be dominant and keep them from having the disease.
EDIT: Allow me to demonstrate.
IOTL, *X=X chromosome with Hemophilia Gene. X=Normal X Chromosome. Y=Y chromosome, of course.
*XX=Queen Victoria, has gene but does not have the disease. XY=Prince Albert. He does not have the gene.
Their spawn could include: XX, *XX (has the mutant gene, but her X chromosome from Albert has the normal gene so she will not express the disease), *XY (Male, will be the only one to express the disease), and XY
IATL, *21=21st Chromosome with Hemophilia Gene, 21=Normal 21 Chromosome.
*2121=Queen Vic, *2121=Prince Albert.
Now, any of their children could be hemophilia free, have hemophilia, or be a carrier, and as the gene is not carried on a sex chromosome, the disease can occur regardless of gender. In short, hemophilia becomes much, much harder to track across generations.
And if they have 212121, they'll have Down Syndrome but that's a different thing.