Just Drew My Gun Defensively For the First Time...Was it Necessary?

I was just walking back from a friends place. I get to my street and maybe halfway down, I see a dog peeking out from behind a fence. It takes only a second to realize that I don't recognize the dog and that it doesn't have a collar. I try very hard not to be "breedist" I guess, but it's a pit bull or pit bull mix of some kind.

As I approach, it starts growling and barking and heading towards me at a trot...pretty quick. Even though I have a box of cupcakes in one hand and an umbrella in the other, I got my Shield out from under a jacket AND t-shirt, thumb safety off, and weapon in some sort semblance of a ready position. Somehow I ended up with the cupcakes and umbrella in my left hand, and had the umbrella down low to sort of block the dog if it got close. This happened very quickly, and I'm honestly pretty impressed with how quickly I was able to respond, especially getting my sidearm out from under all that concealment.

I tried to do my usual "dog deescalation" tactics: talking in an even voice, backing up slowly, and avoiding direct eye contact. The dog stopped running eventually, is still barking, and ducking behind cars. I cross the street, and the dog follows me, and is now in the middle of the street. It's still barking, but seems skittish and less threatening. It's starting to run around and sniff other things, and get excited about other sounds that it hears (like kids and another dog). I felt more comfortable now, and I think this dog is just being silly. I did feel uncomfortable being on my own street with a gun drawn, so by this point I have my Shield in my front pocket with my hand still on it. The dog is still blocking my route home and is still make occasional quick darting runs towards me if I try to go past it. I'm getting ready to call 911 or animal control at this point.

A neighbor is about to leave her driveway, and gets out of her car when she sees the me and the dog. I ask if its hers, she says no, that's Bella and she belongs to Neighbor X, who lives across the street. She promptly scoops up Bella, and delivers her to Neighbor X, who sort of apologized to her I believe (as Bella tries to escape again). I had a bit of an adrenaline dump and really didn't want to get into an argument with the guy about his dog (he seemed like a totally nice guy). Accidents happen.

I wasn't even close to thinking about firing my gun, it was literally the last thing I wanted to do (I'm glad about this in retrospect as well). Did I overreact? Does a dog running at you and barking usually not warrant drawing? Statistically, should I be more worried about a pit bull than a Golden or a poodle? Bella seemed like a total sweetie after the fact, but I just couldn't have known that initially.