A clean camp will be more of a bear deterrence than a fire.
ETA. I've always maintained that every bear is different and that the only predictable thing is they are totally unpredictable; case in point.
4 of us were fishing reds at the mouth of the Newhalen river on lake Llimana Alaska. We flew over and started drinking, cooked steaks in a
cast iron pan got totally drunk, retired to our tents and left the camp a total shithouse.
The next morning we cleaned up, washed the pans, put food away then walked down the trail and slaughtered reds. Just when we got to camp, we saw a Brown bear sow and cub leaving, the camp was trashed, the two 58 qt coolers torn apart, bear teeth imprints all through them, the food was torn up, and what was left was bear slimed.
In short, bears paid no attention to a camp with steak remnants left in the pan, food everywhere and later trashed a clean camp.