Who is the host? If they use Cloudflare (although that usually requires the DNS record to be set to “DNS only”) using a Cloudflare IP address for a record in your DNS seemingly prevents any redirects from taking place.
Otherwise, can you give the real domain and path that should redirect and show a screenshot of your rule?
But I thought the Bulk Redirect rule would/could intercept that before it goes to BigCommerce?
If not, is there a different Cloudflare service I can/should use to accomplish this?