I am trying to make a recipe like this one, Crock Pot Creamy Ranch Chicken, but I do not have dry ranch dressing. Will it still work if I use ranch dressing from a bottle instead? Would I need to change anything else?
It will likely work, but the flavors will be muted. At a minimum, I would leave out the milk in the recipe. You might be better off using other dried herbs and spices, even if they aren't specifically 'ranch'. The recipe in question links to a recipe for making ranch dressing mix, which is black pepper, dill, garlic, onion, parsley and salt.
The advantage of dry mixes is that they have a lot of flavor, without any liquid to water things down.
As the recipe stands, the liquid would be from the milk, condensed soup and the liquid that the chicken exudes as it cooks. To get the same amount of ranch flavor in the dish as you'd have gotten from the dry mix, you'd have to use as much as the dry packet would make ... which is typically a couple of cups of dressing ... and that can be a lot of liquid to add to a dish.
In addition, the extra dairy will mute the flavors some, and it'll be a bit more soupy -- you'd likely want to serve it over pasta or rice to help absorb some of the sauce.