I'd guess it dates to around the 1920s-40s, tough to narrow down beyond that. What strikes me as interesting is the "Bottle property of..." message on the bottom. Did Ed Pinaud have deposit bottles? Not something I've ever heard of before for perfume/cosmetic bottles, although I wonder if barber bottles might have had deposits on them. Yours is an interesting large design I've never seen before for a Pinaud, I could definitely imagine this sitting in a barbershop.
The bottle was made by Hazel-Atlas. The "H" over a smaller "A" is said to have been first used in 1923. I am unaware of the meaning of the numbers adjacent to the Hazel-Atlas mark. Yours has "3" to the lower right of the glass mark. Personally, I believe them to be single-digit date codes like Owens-Illinois. If this were to be true, your bottle could have been made in 1923, 1933, 1943, or 1953. I have no idea if this is true or not, this is a personal belief. Really cool bottle nonetheless.