Generate your controller skeletons in SceneBuilder.
In SceneBuilder, create your FXML, then:
View | Show Sample Skeleton
Press the "Copy" button.
File | New Project | JavaFX Application
Click on your src folder.
Paste (e.g. CMD+V on Mac).
File | Save As
Save your fxml into the same src directory as the Controller Skeleton you just pasted.
Modify the Controller Skeleton and your Main Application as needed.
Run the program in Idea.
If you make subsequent changes to the FXML, use View | Show Sample Skeleton again to generate new Controller code, then manually copy and paste in the bits you want into your controller.
Generally, I try to keep FXML files pretty lean of any custom code I write (or at least not mix the custom code with the skeleton code), so that it makes it easy to just copy and paste skeleton changes into them.
I don't like Ruby, but I like the way JRubyFX handles FXML (it automatically generates the controller skeletons from the FXML). Unfortunately, nobody has created equivalent functionality in Java.