This question really made me curious as my wife has asked me the same thing. If you end up finding a better solution than anyone on this site can provide, I ask that you would please share it.
I searched the web for a bit and found this website.
Allow me to quote the part I found most important.
Sponges Isabelle Gauthier of Blood Sisters, an organization of women in Montreal,
created a publication called Hot Pants which describes the use of sea
sponges for menstruation. Often sold as cosmetic sponges in pharmacies
sea sponges can be inserted into the vagina and can be left inside
until saturated. The sponges should be soaked overnight in water with
white vinegar before and after each period. It is necessary to dispose
of the sponge in the garbage once it begins to fall apart.
Pros: This option is environmentally friendly and chemical free.
Cons: Being aware of the saturation level of your sea sponge may be
the last thing on your mind as you portage across a rushing creek.
Although Gauthier insists that the sponge will not get lost "up there"
it may be difficult for some to get used to reaching up to extract the
sponge. There may not always be fresh water available to rinse your
Cost: Pharma Plus sells a bag of 3 natural sea sponges for $6.49.
Gauthier approximates that a single sponge could last "six months if
you take good care of it." A lifetime of menstruation could be yours
for just over $100.00
Article: How to Handle your Period while you Enjoy the Great Outdoors
Author: Beth Clarkson
Upon further investigation, you should take care to thoroughly clean the sponge before first use and subsequent uses (obviously). This site notes they are no longer sold as hygiene...things... (not sure what to call them) as they have been known to contain bacteria.
Here's the relevant stuff:
Your concern about ocean pollution making sea sponges potentially
dangerous is justified. In fact, this is the reason sea sponges are
technically no longer allowed to be sold as menstrual products. In
late 1980, menstrual sponges sold commercially were examined by a
University of Iowa laboratory and found to contain sand, grit,
bacteria, and various other contaminants. Other studies have found
chemical pollutants and fungi in sponges sold for menstrual use. The
Centers for Disease Control have documented a least one case of toxic
shock syndrome associated with the use of a sea sponge.
Article: Menstrual cycles and sea sponges
Author: John Robbins
The more I research about this issue (which I should probably stop now) the more I see that most women vastly prefer a menstrual cup, particularly the Diva Cup
Just ran across this article about bears and menstruation. It is hypothesized that the odors from used tampons and pads attract bears. If bears are attracted to them, my very uninformed opinion is that other carnivorous animals may be attracted also. So I hope that immediately eliminates the use of pads and tampons for you.
Article: Bears and Menstruating Women
Author: Kerry A. Gunther