I found a solution for my problem. The new way to hook into the application start seems to be implementing the IApplicationEventHandler like so:

namespace MvcUmb410plus
{
    public class MyApplication : Umbraco.Web.IApplicationEventHandler
    {

 #region IApplicationEventHandler Member


        public void OnApplicationStarted(UmbracoApplication httpApplication, Umbraco.Core.ApplicationContext applicationContext)
        {
            Bootstrapper.Initialise();
        }

        public void OnApplicationInitialized(UmbracoApplication httpApplication, Umbraco.Core.ApplicationContext applicationContext)
        {
        }

        public void OnApplicationStarting(UmbracoApplication httpApplication, Umbraco.Core.ApplicationContext applicationContext)
        {
        }

 #endregion
    }

    //public class MyApplication : Umbraco.Web.UmbracoApplication
    //{
    //  protected override void OnApplicationStarted(object sender, EventArgs e)
    //  {
    //    base.OnApplicationStarted(sender, e);
    //    Bootstrapper.Initialise();
    //  }

    //}
}