While I'm not too familiar with Bundles, have a look at the documentation for attaching to events, that happens during the Initialization of Umbraco so hopefully works for you:

https://our.umbraco.com/documentation/Implementation/Composing/#example---creating-a-component-to-listen-for-contentservicesaving-events

Example code could look a bit like:

using System.Web.Mvc;
using Umbraco.Core;
using Umbraco.Core.Composing;

namespace MyProject.Components
{
    [RuntimeLevel(MinLevel = RuntimeLevel.Run)]
    public class MyComposer : IUserComposer
    {
        public void Compose(Composition composition)
        {
            composition.Components().Append<MyComponent>();
        }
    }

    public class MyComponent : IComponent
    {
        public MyComponent()
        {

        }

        public void Initialize()
        {
            AreaRegistration.RegisterAllAreas();
            BundleConfig.RegisterBundles(BundleTable.Bundles);
        }

        public class BundleConfig
        {
            public static void RegisterBundles(BundleCollection bundles)
            {
                bundles.Add(new StyleBundle("~/bundles/site.css").Include(
                    "~/css/style.css"
                ));
            }
        }

        public void Terminate()
        {
        }
    }
}

Thanks a lot! :)

Regards Josefine

Just delete MyComponent, else there will be a return null error:

using NAMESPACE.App_Start;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Web.Optimization;
using Umbraco.Core;
using Umbraco.Core.Composing;

namespace   NAMESPACE.Components
{

    [RuntimeLevel(MinLevel = RuntimeLevel.Run)]
    public class MyComposer : IUserComposer
    {
        public void Compose(Composition composition)
        {
            composition.Components().Append<BundleComponent>();
        }
    }

    public class BundleComponent : IComponent
    {

  public void Initialize()
  {
   BundleConfig.RegisterBundles(BundleTable.Bundles);
  }

  public void Terminate()
  {
  }
 }
}

Also place bundleconfig in APP START

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Web.Optimization;

namespace NAMESPACE.App_Start
{

        public class BundleConfig
        {
            public static void RegisterBundles(BundleCollection bundles)
            {
            bundles.Add(new StyleBundle("~/bundles/css").Include(
                "~/css/screen.css"));

            bundles.Add(new ScriptBundle("~/bundles/app").Include(
                                "~/_publish/scripts/app.js"));          


        }
    }
}

Remember webconfig:

 <add key="Umbraco.Core.ReservedPaths" value="~/bundles" />

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