How can I specify an explicit ScriptBundle include order?

You could write a custom bundle orderer (IBundleOrderer) that will ensure bundles are included in the order you register them:

public class AsIsBundleOrderer : IBundleOrderer
{
    public virtual IEnumerable<FileInfo> OrderFiles(BundleContext context, IEnumerable<FileInfo> files)
    {
        return files;
    }
}

and then:

public class BundleConfig
{
    public static void RegisterBundles(BundleCollection bundles)
    {
        var bundle = new Bundle("~/bundles/scripts/canvas");
        bundle.Orderer = new AsIsBundleOrderer();
        bundle
            .Include("~/Scripts/modernizr-*")
            .Include("~/Scripts/json2.js")
            .Include("~/Scripts/columnizer.js")
            .Include("~/Scripts/jquery.ui.message.min.js")
            .Include("~/Scripts/Shared/achievements.js")
            .Include("~/Scripts/Shared/canvas.js");
        bundles.Add(bundle);
    }
}

and in your view:

@Scripts.Render("~/bundles/scripts/canvas")

Thank you Darin. I've added an extension method.

internal class AsIsBundleOrderer : IBundleOrderer
{
    public virtual IEnumerable<FileInfo> OrderFiles(BundleContext context, IEnumerable<FileInfo> files)
    {
        return files;
    }
}

internal static class BundleExtensions
{
    public static Bundle ForceOrdered(this Bundle sb)
    {
        sb.Orderer = new AsIsBundleOrderer();
        return sb;
    }
}

Usage

bundles.Add(new ScriptBundle("~/bundles/jquery").Include(
                    "~/Scripts/jquery-{version}.js",
                    "~/Scripts/jquery-migrate-{version}.js",

                    "~/Scripts/jquery.validate.js",
                    "~/Scripts/jquery.validate.messages_fr.js",
                    "~/Scripts/moon.jquery.validation-{version}.js",

                    "~/Scripts/jquery-ui-{version}.js"
                    ).ForceOrdered());