Hi
Neither NinjaFirewall nor CloudFlare should block Bing. As you mentioned, you deleted the plugin and disabled the CDN, thus the problem is elsewhere.
Go to Bing webmaster and use the “Fetch as Bing” to fetch a couple of your pages. Then, search in your HTTP server access and error logs for those Bing requests. Then, there are 2 possibilities:
1. You can see the HTTP requests in your logs:
Check the return code (200, 503, 404 etc). You may have another security plugin that blocked it, or a plugin that added code to your .htaccess etc.
Check your HTTP server configuration as well.
2. You cannot see the requests in your logs:
Check your SSL certificates, openSSL version and HTTPS vhost configuration (ensure you aren’t using an old TLS version etc).
Check Bing’s forum, it seems there are similar discussions about Bing and HTTPS (e.g.: Bing de-indexed entire site after switching to https).