There are a number of issues that could be causing this.

What technically is happening in most of these cases is that the configured bridge URL does not match the URL being called, so the bridge helper is trying to redirect you to the correct bridge URL. 

Please go through the following check-list.

1. Make sure you have installed the latest version of all 3 plugins: (1) The WHMCS Bridge SSO plugin (2) The BridgeWP addon for WHMCS and (3) The base WHMCS Bridge plugin. 
2. If your are using HTTPS, please make sure you have precisely followed the full instructions located here: https://i-plugins.com/whmcs-bridge/knowledgebase/1037/How-do-I-set-up-SSL.html/
3. Please make sure your WHMCS General Settings page does not have a URL for "WHMCS SSL System URL", if you want to use SSL please see point # 2. 
4. Note: This is only required on some installations: If you are using HTTPS, you may need to update your WordPress URL to the HTTPS version of your domain (WordPress Admin -> Settings -> General -> WordPress Address & Site Address). 
5. In your WHMCS Addon configuration (WHMCS Admin -> Setup -> Addon Modules -> WHMCS Bridge Helper -> Configure) please make sure that the URL entered for your WHMCS Bridge page URL matches EXACTLY the URL generated by our WordPress plugin (located on the "Help" tab of the Settings -> WHMCS Bridge page). 

If you have gone through all of the above steps thoroughly please submit a support ticket, we will likely require a temporary login to your WP admin and your WHMCS to further debug this issue.