Nature Photographer at Work (Really!)
To put concerned bystanders at ease, you want to make sure they understand the situation. So the most effective message is likely to be a direct one.
Colorful jokes may work sometimes, but if people don't understand what's going on, they may feel compelled to verify.
I'd suggest having the same, direct message on a yard ...
Scootbb has a great answer, but I would suggest that you have some custom shirts, hoodies or jackets made for her with wording on the back. Bonus points for you if you give them to her as a gift.
On the back it could say "I am not dead or injured, just taking photos" or any wording you feel is appropriate.
This may preferable to carrying a sign.
While this is a rare instance of need, it's a shame there isn't a photographic equivalent of the red field with white diagonal stripe "diver down" flag, or the more internationally-recognized blue-and-white "Alpha" flag.
Perhaps she could fashion her own "photographer in action" sign, with a combination of symbols for instant ...