I have a Whites Bullseye #1 also, and it was giving false alarms also, it was beeping when I would just wave it in the air, until I finally got it adjusted correctly, now it works fine. The range is not very far, maybe an inch on dimes at best, which is good if hunting in damp ground where a coin can be hidden in a small clump of wet dirt.
I got to try a new Whites Bullseye #2 last weekend, and it has the sensitivity adjustment on the outside, which makes it easy to adjust the sensitivity now. It also doesn't give false signals while moving it around or bumping it against the side of the hole you have just dug like the old one does sometimes if not adjusted properly. I also like the push button on the new one, it is larger and fits the thumb nicely, and the light helps also to see down in the hole, plus it is narrower and fits the hand better. One thing it needs is a belt clip of some kind. Maybe Bullseye #3 will have a built in belt clip. HH Scotty