i always bell my setters- even though i can't hear one very far any longer, i use a garmin gps tracking collar now for back up in case they get out of hearing range ( 20 feet or so
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personally - i think whether it bothers the birds or not depends on a lot of factors - over pressured birds get spooky- and some of my setters, as with my Osthaus, would hit a point at full speed and pin a bird right there - I really do not think the bell affected them- Griffin is a slower moving dog and i would not be surprised it give some birds a warning. i can't say i have seen it make a difference in their hearing a command.
side story - i was showing my son around the deer sign (he bow hunts) in one of my woodcock covers and we ran into a couple other deer hunters in the parking area - they were telling me about seeing some guy and young girl hunting "rabbits" with a big white dog wearing a bell - they thought that was the silliest thing they had ever seen. I didn't bother to tell them that was me and my oldest daughter that day , and we moved plenty of woodcock while "rabbit hunting"