My #1 rule when approaching shy dogs is don’t approach shy dogs. A major reason I
have gotten through 30 years as a professional dog trainer without scars or major mishaps (so far) is that I respect the dog. If a dog is frightened, I respect that. Just as I would respect a person who was frightened. I introduce myself gently at a distance and, if the dog shows no interest/willingness to interact, I respect their wishes.
At that point, I’ll turn sideways (to be less threatening and if a dog is frightened then your very presence is threatening), chat with the human and ignore the dog. If the dog makes their way over to me, I continue to ignore the dog while they sniff me.
If they linger after sniffing, I may lower my hand a distance in front of them to sniff it, if they want to. Or not. And if they sniff it and then linger some more, I might scratch their chest or under their neck gently and briefly, always trying to end my contact before they move away from me.
At that point, I might shift my body away (to remove any pressure they may be feeling by my proximity and to show them I respect their concerns) or even walk away a few steps. If I’ve done my work well, the dog will follow me and we will repeat this dance a few times until they relax and decide I am exactly what I am: a friend.
Reaching your hand into their space, leaning in at them, trying to force yourself onto a shy/nervous dog to “prove” your good intentions is an excellent want to get bitten and, in my world, disrespecting the very animal you love.
By respectfully working with the dog where they are, you’ll get to where you want to go—to friendship—faster than force. Any day and every day.