Hope this answers some of your questions:
On shark attack:
Over the 3-5 days of menstruation a woman is likely to lose between 50mls and 150mls of blood and cellular debris. This is an extremely small amount of stale and congealed blood (further plugged with a tampon or a pad, and wrapped up in a wetsuit or dry suit), however over the years many female divers have expressed fears that sharks may be attracted at this time. You'll be glad to know that there are no studies to support this belief, and when looking at shark attack statistics from around the world women actually have a much lower incidence of attack than men.
I've run shark diving charters for over 11 years and have never once seen any aggression from sharks underwater, towards men or women. We've completed thousands and thousands of open water cageless dives with schooling 3-4m long hammerheads, 5-6m tiger shark, 3-4m zambezi shark, 2-3m raggged tooth shark, etc. We've people who are even just starting to free dive with great whites, and not a single sign of aggression or danger anywhere. I think that we've learned over the years that so much of our fear of shark is driven by ignorance and misunderstanding.
Further, we've found sharks are very fickle when it comes to their eating habits - to attract great whites with chummed fish, meat, and blood products, as happens in numerous locations worldwide, the blood and meat products have to be very very fresh and in large quantities. Sharks don't like humans, that's been demonstrated time and time again (we're too boney and the yellow bits on our backs make them fart - chuckle).
Some further comments on menstruation and diving: Repeated exposure to hyperbaric pressure seems to have no effect on hormone regulation, ovulation, or menstruation. Some women suffer from premenstrual fluid retention and have reported changed buoyancy control. Other women may get congestion of the mucosal membranes, and when this happens it may be more difficult for the affected woman to clear her ears and may also predispose her to sinus barotrauma.
Women make fantastic divers, they've better breathing rates than men generally and can thus stay underwater longer, and they're more aware and appreciative of the underwater environment. They make fantastic Divemasters and Instructors, with their abilities, empathy, and patience. Tell her not to fear, she'll be a great diver and will absolutely love it. Your only issue to explain will be why you never introduced her to the sport earlier!
I've been diving for over 16 years, and have dived & taught courses in South Africa, Mozambique, Maldives, Egypt, Jordan, Scotland, and England.
kind regards
Dennis Guichard
NAUI Instructor Trainer
IANTD Technical Instructor
HSE Commercial Offshore Diver Medic
IMCA Saturation Life Support Technician
Red Cross Paramedic (level 4) Primary Emergency Care
ASHI First Aid Instructor