Found a dev reply on reddit from a few years ago on how to obtain the Fearless Bonus:
"It consists of a variety of factors, but (without trying to be too vague) it's awarded for driving 'fearlessly'. Running the stage fast, on the edge of control, going for the gaps, and pushing to the limits should net you a fearless bonus."
So the easiest set up for this is:
1.) Main Menu
4.) Add Event
6.) Add Stage
7.) Move the slider for "Length" and "Complexity" all the way to the left
to Generate the Stage
10.) Confirm again
11.) Start(Change vehicle if you want)
12.) Run the race
It will take ~1 min to finish the stage. As this is made with a short and minimally complex stage, you are free to go flat out for pretty much the entire stage. I generated a couple different stages using those parameters, and at most all I had to do was let off the gas to keep it inside the corners.
And here's the reddit thread if anyone wants to see it from the dev: https://www.reddit.com/r/dirtgame/comments/6gqcmn/fearless_b...