TeXworks doesn't do any downloading of missing packages. You're probably relying on MiKTeX's ability to download packages if they aren't yet present on your local system. I don't really know much about this automatic download feature, but it may possibly fail for some package.
bitset package is part of the so-called "oberdiek bundle", which includes most of the packages developed and maintained by Heiko Oberdiek.
The MiKTeX page for the package is http://miktex.org/packages/oberdiek and the package can be installed with the MiKTeX Package Manager.
On TeX Live distributions, the name is the same and the maneuver for installing it with
tlmgr install oberdiek
It's not recommendable to install it alone, because you would miss updates, so install the whole bundle. As Ryan Reich remarks, most of these Oberdiek's packages rely on other package in the same bundle. It's the case for
bitset that requires
bigintcalc; the last one requires
pdftexcmds, which wants
ifpdf. So, taking care of all these dependencies is longer than downloading the whole set.
If disk space is not a problem for you, I suggest to do a full install of the whole TeX distribution (MiKTeX or TeX Live) and to regularly check for updates.