Note: There is a bootstrap jQuery plugin that does this and so much more that was introduced a few versions after this answer was written (almost two years ago) called Affix. This answer only applies if you are using Bootstrap 2.0.4 or lower.
Yes, simply create a new fixed class for your sidebar and add an offset class to your content div to make up for the left margin, like so:
Fixed my demo to support the responsive bootstrap sheet, now it flows with the responsive feature of the bootstrap.
Note: This demo flows with the top fixed navbar, so both elements become position:static upon screen resize, i placed another demo below that maintains the fixed sidebar until the screen drops for mobile view.
minor note: there is about a 10px/1% difference on the width of the fixed sidebar, its due to the fact that since it doesn't inherit the width from the span3 container div because it is fixed i had to come up with a width. It's close enough.
And here is another method if you want to keep the sidebar fixed until the grid drops for small screen/mobile view.
With the current Bootstrap version (3.3.2) there is a nice way to achieve a fixed sidebar for navigation.
This solution also works well with the re-introduced container-fluid class, meaning it is easily possible to have a responsive full-screen layout.
Normally you would need to use fixed widths and margins or the navigation would overlap the content, but with the help of the empty placeholder column the content is always positioned in the right place.
The below setup wraps the content around when you resize the window to less than 768px and releases the fixed navigation.