Register a CDN URL generator for Cassette. See blog post: http://kamranicus.com/blog/2015/10/10/azure-cdn-cassette/

CassetteConfiguration.cs

namespace Website {   

    /// <summary>
    /// Configures Cassette IoC
    /// </summary>
    public class CassetteContainerConfiguration : IConfiguration<TinyIoCContainer>
    {
        public void Configure(TinyIoCContainer container)
        {

            // set CDN support
            container.Register<IUrlGenerator>(
                (c, n) =>
                    new CdnUrlGenerator(c.Resolve<IUrlModifier>(), c.Resolve<CassetteSettings>().SourceDirectory));
        }
    }

    public class CdnUrlGenerator : IUrlGenerator
    {
        private readonly IUrlGenerator _urlGenerator;

        public CdnUrlGenerator(IUrlModifier urlModifier, IDirectory sourceDirectory)
        {
            _urlGenerator = new UrlGenerator(urlModifier, sourceDirectory, "cassette.axd/");
        }

        public string CreateBundleUrl(Bundle bundle)
        {
            return GetCdnUrl(_urlGenerator.CreateBundleUrl(bundle));
        }

        public string CreateAssetUrl(IAsset asset)
        {
            return GetCdnUrl(_urlGenerator.CreateAssetUrl(asset));
        }

        public string CreateRawFileUrl(string filename, string hash)
        {
            return _urlGenerator.CreateRawFileUrl(filename, hash);
        }

        public string CreateRawFileUrl(string filename)
        {
            return _urlGenerator.CreateRawFileUrl(filename);
        }

        public string CreateAbsolutePathUrl(string applicationRelativePath)
        {
            return _urlGenerator.CreateAbsolutePathUrl(applicationRelativePath);
        }

        public string CreateCachedFileUrl(string filename)
        {
            return _urlGenerator.CreateCachedFileUrl(filename);
        }

        private string GetCdnUrl(string relativeUrl)
        {
            string url = AppSettings.CdnUrl.TrimEnd('/') + relativeUrl;

            var ctx = HttpContext.Current;

            if (ctx != null)
            {
                var ctxBase = new HttpContextWrapper(ctx);

                // for SSL context, request HTTPS URL otherwise HTTP
                // because CDN Origin needs to match
                if (ctxBase.IsSSL())
                {
                    url = url.Replace("http://", "https://");
                }
                else
                {
                    url = url.Replace("https://", "http://");
                }
            }

            return url;

        }

        /// <summary>
        /// Prepends the CDN URL if given
        /// </summary>
        public class CdnUrlModifier : IUrlModifier
        {
            public string Modify(string url)
            {
                url = url.ToLowerInvariant();

                if (url.StartsWith("http"))
                {
                    var ctx = HttpContext.Current;

                    if (ctx != null)
                    {
                        var ctxBase = new HttpContextWrapper(ctx);

                        // for SSL context, request HTTPS URL otherwise HTTP
                        // because CDN Origin needs to match
                        if (ctxBase.IsSSL())
                        {
                            url = url.Replace("http://", "https://");
                        }
                        else
                        {
                            url = url.Replace("https://", "http://");
                        }
                    }

                    return url;
                }
                else
                {
                    return "/" + url;
                }
            }
        }
    }
}

web.config

<configuration>
  <appSettings>
    <!-- Local Setting -->
    <add name="CdnUrl" value="cassette.axd/" />
    
    <!-- Azure/Production -->
    <add name="CdnUrl" value="https://az9999999.vo.msecnd.net/" />
  </appSettings>
</configuration>

How do you handle the hash in the url? For example:
https://az9999999.vo.msecnd.net/script/d81ab7428c71bfd2d3433ebd29a944bd3eef6d9e/js/somejs

How do you handle the bundled js?