We don't actually know if Nausicaa wears underwear, but no, I do not believe we're staring at her naked bottom throughout the entire movie.
In the manga covers, you can see pretty clearly that she's wearing white pants under her skirt:
Not only is the manga the original work that the movie was based on, it was written and drawn by Hayao Miyazaki himself. (It's right there on the cover—story and art by Hayao Miyazaki. Wikipedia also confirms.) I don't know why he would have changed that between the manga release and the anime.
However, I won't deny that her pants in the anime are cream-colored and seem to be tighter fitting, which definitely makes it look like she's not wearing anything under her skirt:
I have seen the DVD release and can also attest that this is the same in the DVD. According to this review, it's actually the Blu-ray release that cleans up the colors:
Having never acquired the DVD release of Nausicaä due to it being a low priority. The faded quality of the version I first saw years ago probably had a lot to do with it. In 2011, Disney released the Blu-ray and last year I decided to fill a gap in my collection. That turned out to be a great decision.
Disney’s first Studio Ghibli Blu-ray release includes the movie on DVD and is of the digitally restored version. Suffice it to say this is the best the movie has ever looked in the States. The movie is presented in anamorphic widescreen in 1.85:1 ratio for both discs while the Blu-ray is in 1080p High Definition.
It is absolutely gorgeous with the colors finally being faithful. This is important due to prior releases making it look like Nausicaä wasn’t wearing any pants or underwear! The color of her pants were too close to the skin tone used and got lost in the mastering before this release.
Here is a gallery of images from the Blu-ray release. We can see that, while the pants are still not as white as in the manga, they are definitely a different shade from her face:
I wouldn't say that Ghibli films have "a bias against prudishness". They'll show underwear or a bath scene if it makes sense to show it, but by anime standards, they're quite sparing with nudity and sexual themes. Miyazaki himself is usually considered a feminist; here is one of many articles I found praising the feminist themes in his work. Even without all the other evidence, it just doesn't feel in character for Miyazaki to draw a heroine with no pants and no underwear running around exposing her naked rear end through an entire movie. So even if all we had was the DVD release and didn't have the Blu-ray or manga to suggest it to us, my vote would still go to "no, she's wearing pants".