According to Cowboy Bebop's wikipedia page:
Bebop received universal critical acclaim and won the renowned Seiun Award in 2000, a Japanese science fiction award for the best science fiction work published during the preceding year, as determined by the Japan Science Fiction Convention. It was named Best Media of the Year by the Science Fiction Convention.
In 2006, the Japanese MiniTokyo review claimed, "To say nothing more, it is a masterpiece, a genre defining series that has a right to be held in such high confidence. Not many series can do even one of the elements as well as Cowboy Bebop does, and even fewer can actually get every single solitary aspect of themselves to such a high degree of excellence. Everything in this anime falls into place with such perfection that makes it all organic and real and following to the extent that they do. From the full gamut of emotions to the roughs and roughnecks of the Bebop, to the masterful soundtrack that gives life to many of the episodes themselves, to the art that so perfectly conveys the mood and atmosphere of the entire work. Cowboy Bebop is not an anime to be missed, and not to be forgotten."
So it was well received, but unlike other franchises that continue to have new TV series, manga, novels, merchandise, or even doujin, Bebop is a one shot 26 episode series with a movie shortly after the airing and that's about it. It aired during a time when you didn't have massive blocks of anime on every channel, so most people probably didn't think that much about it. There's still a prevalent conception that anime is most stuff for kids eventhough that's not the case anymore, and being labeled an otaku of any kind is a social stigma.
Most people probably wouldn't know of a show that aired over 10 years ago, that only aired half of the show, and didn't have many more re-airings (except maybe on Friday Road Show, I'm not sure where to find this information). Most people probably would never had heard of "Macross" or "Gundam" if it wasn't for the franchise churning out products, and thus, having advertisements placed all over the place. Most people probably never heard of shows like "Legend of the Galactic Heroes" for similar reasons.