One of my best friends kept a "bag" as he called it in his pickup all the time. I used to tease him and say 'no dude! THAT'S a purse!"

Of course I don't now to many women who carry in their "bags" what he carried! A bottle of black jack, a Smith & Wesson .357 magnum, a dozen condoms, three packs of Marlboros, and six one hundred dollar bills.
Of course I may be wrong. There's probably LOTS of women who carry such things!
(get the bag, man. I'm not disparaging your interest in one!lol....)