Bears in Requiem do have a warning distance (they had one in vanilla too, but it was never properly implemented). So long as you don't threaten it by drawing a weapon or moving closer in its threat zone, it should just stroll on by.
Sabre cats, now...that's a different story. They will be actively stalking you through all that grass. They have a delightful knockdown attack, btw.
Funny story: just before quitting I turned away from that bear and there was a dead Sabre Cat behind me. Following Faldrus from Rorikstead to Whiterun paid off as a survival strategy.