The few times I've sampled FNR, I didn't notice much of a bias either. I think the problem is more the toxicity of the Fox brand among liberal listeners; in other words, they will refuse to pay any mind to anything with the word Fox in its name, especially if it's news related.
The bias can be there but difficult to see. Let's pretend the top 10 news stories in the current hour are: A, B, C, D, E, F, G, H, I, J. CBS's newscast airs A, B, C, D, E, F, maybe G if enough seconds remain in the cast.
Fox looks at the same stories and airs A, C, E, F, H, J. If you listen to a Fox newscast, you'd never know B, D, G or I had happened. Why? Because those latter stories don't fit the narrative Fox wants to sell you. Bias by omission.
NPR does what CBS does, only they give more seconds to each of the biggest or newest news stories. So in their case it might be A, B, C, D, and if time permits E. Not enough time in the current hour to squeeze in the other stories. But E, F, G, etc. might have gotten the full treatment in earlier newscasts, and in any event all of those stories were (or will be) covered on Morning Edition and/or All Things Considered and/or Here and Now.