Just a few comments on above answers since I don't have enough rep. to comment directly...
The answer from Hainesy suggests using a BundleTransform. I believe this is too late in the process to include an embedded resource. The BundleTransform is helpful for converting things inside the css or javascript after the contents are pulled from the original file and before they are put into the bundled file. For example, if you need to modify image URL's in CSS to point to local relative url for dev and to a CDN url for production.
The link from user960567 explains how to use embedded resources, but there's a catch. That process will only work for something like a common control used from another project.
e.g. If you create a textbox that needs CSS and JS then it allows you to create a HTML helper in the common project that will add the textbox and the script tags that pull in the embedded resource into the page. It does not allow you to pull the embedded resource from the common project into a bundle in another project. This will basically create a separate script or style tag for each embedded resource which may not be what you want (at least it's not what I was looking for.)