Here is the link to the official docs for Bootstrap versions: http://bootstrapdocs.com/
Looking at Browser support for Bootstrap 1.1.0 it says Internet Explorer 7+. The docs for the earlier version v 1.0.0 (which was the first public release) doesn't even mention supported browsers. You can check if more recent version added support for IE6, but I don't think so. I also discourage using an old version at all.
If you can chose another framework I'd suggest YAML, it is actively maintained, well documented and supports IE6, too.