Without really getting in the weeds this is what I’d do:
Create a dataview for your BAQ, use the guided setup to create the dataview and it will walk you through setting a filter to tie it to the existing data (like if your baq has case number and you want to return the result from the baq that matches the current case you’re on.) The guided setup will also create an event called yourbaq_Get that you’ll use later.
Figure out how you want to trigger the baq, a button, an On-blur event from another field whatever, and then from that trigger do an event-next to the yourbaq_Get event, then a row-update widget to write the result from the baq dataview to the field in case entry.
Just throwing this out there: start with a button event. That is the most reliable, repeatable way to make sure you are firing your event logic. I have seen oh so many times when you think the event is doing what you’d expect but in the end, it just doesn’t. OnBlur has been one for me that I have had very mixed results with. So get it working with the button click, then hook it to an event-next widget in the event you want it to actually fire from and make sure that’s working properly too. Then obviously you can get rid of the button.