In those days, most women DID douche!
There were many more styles of nozzles available in drug stores than there are today.
The “Bat” douche nozzle may or may not have been used for enemas in some cases.
It is typically not very suitable for enemas, because it's small holes can so easily become clogged with poop so deep that it takes a rather large sewing needle to get them open. Truly clean is even harder!
Don't forget, it was designed to carry a relatively thin solution such as Massengill or iodine, not something thicker like soap, glycerin, or similar.
Also, most women seemed to prefer douching either sitting on the toilet, or crouching in the shower
That reclining in the bathtub position shown shown in the “women's health” books of the era was not really used by most women.
In a sitting or squatting position the vagina has a curve to it that is much more like that of most of the curved nozzles than straight like is would be in the reclining position. Given that, from about 1968 on most bags came with the straight nozzle included, some may have been re-purposed for enemas, especially in households where the curved nozzle was preferred. Probably with barely satisfactory results!