There is currently no separate plugin to integrate The Bug Genie with Jetbrains' WebStorm / PhpStorm, etc suite of products. However, you can add The Bug Genie as a generic issue tracking / task server to add support for working with issues in The Bug Genie as tasks in WebStorm (we'll refer to WebStorm from here on out, but the approach applies to all Jetbrains' IDE products).
For more information on how to add a generic task server in WebStorm, see JetBrains' online documentation.
On the General tab, input the address of your The Bug Genie instance (works for both paid hosted instances and self-hosted instances), as well as your username and password. Make sure the "Login Anonymously" box is checked.
Before you continue, you need to create an application password for WebStorm in The Bug Genie. Log into The Bug Genie and go to "Your account" -> "Security". Click the "Actions" button on the "Application passwords" header and generate a new application password. You can name it something like "WebStorm task server", but remember to copy the password that is displayed (it only shows once). Use that password as the token in the url below.
In WebStorm, on the Server Configuration tab, enter the following value in the "Tasks List URL" input box, replacing project_key with the project key in The Bug Genie, username with your username in The Bug Genie, and token with the password you just copied (don't replace the curly bracket values, they will be interpreted by WebStorm):
Leave the "Each task in separate request" checkbox unchecked. As the last step, select JSON as the "Response Type", and fill out the following values to tell WebStorm which details to look for:
Now, press the "Test" button to make sure WebStorm is able to communicate with The Bug Genie properly.
When completed, you can now use the task integration in WebStorm.