If it’s bernardii, odor should be briney or like iodine. Reddening fits, as does the membranous veil and short tapered stipe. It should also be quite hard, and in my experience, the cap will frequently crack with age. Often found near salt water habitat, on disturbed ground, grass, etc. Excellant edible!

Check out Fred Steven’s fine work on this species (and many others in genus Agaricus) here:
http://www.mykoweb.com/CAF/species/Agaricus_bernardii.html