Good thinking! I had suggested previously that it was simply a pretext, for which I was given 50 lashes with a wet noodle, but your concepts make total sense.
I can see it being used as an explanation for something to have been cleaned with bleach. Most little stores in that area carry small 20oz (soda or water bottle) sized containers of bleach, laundry soaps & stuff. Backpackers coming through the area wouldn't be carrying it so they would just purchase small amounts wherever they find a place to do wash. That could be one of the items they purchased, which is why that is all such a big secret.
I don't know if it is odd that she would text her mom about it or not? I can see how it would easily come up in conversation though. As for not having a supply with her? Well, I usually have a few stashed here & there. I even keep a couple in my husbands vehicle. But when I run out & don't want to go to the store I go right through my backup supply & then am totally out. Its also possible that she just forgot to pack them. Regular people forget obvious things all the time- that is why hotels always have toothbrush and deodorant at the desk. To me, as a woman, the lack of preparedness & talking about it isn't weird in itself.
I do want to point out, in case some aren't aware, that menstrual blood isn't just blood. Under a scope it would be obvious that it was menstrual. There would be mucous and endometrial cells from the lining of the uterus.
The explanation of menstruation would have to be used to cover a very small area of blood staining. Even overnight we are likely talking about less than 1/4 c of blood. If it were a larger area or somewhere other than JM pants/sleeping bag/or seat then it would be very odd to investigators right away. Of course JM & DK aren't coming across as real bright, maybe they think that all the men in LE and SAR would just back off the minute a "woman issue" was given. SB might be a conservative good ole boy, but he is also been married to a woman for a long time and not an idiot. If there was more than a couple spots or in a bizarre place he would think to check. Especially after day 3, when alarm bells were clearly going off.
Even after cleaning with chlorine bleach, DNA and cellular evidence could still be present. Especially if it was cleaned up in a hurry by someone who didn't really know what they were doing.
If they used oxy-bleach or peroxide it would be totally gone. Peroxide is great at getting blood stains out of scrubs & off shoes.