Soda cools faster in an ice bath because water has a really high heat capacity. What that means is that water or ice need a lot of thermal energy to increase its own temperature.

Remember this: heat always flows from hot to cold. So, when you think of an ice bath cooling something, its not that the ice water is making your drinks colder, but that your drinks are making your ice water hotter. The drinks usually can’t compete with the amount of heat that the ice water absorbs, and will become roughly the same temperature as the ice bath. Also, another important part is that ice will always stay at 0 degrees C while it melts. So if you have an ice bath that still has ice in it, it has to be 0 degrees C or lower.

All the best.
heat capacity

Water is a much better conductor of heat . If you have ever stepped into a pool that is the same exact temperature as the air outside, you may have noticed that it still feels cooler than the air around you. This is because water is very efficient at pulling the heat away from your body.

The laws of thermodynamics (fancy word for heat and energy) state that everything in the universe wants to reach an equilibrium. So, for example, if you leave your warm soda inside a cool refrigerator, the heat will eventually escape until both the fridge and the soda are at the same temperature. If the soda can is surrounded by a liquid, this process will happen much faster.

The key to your question is heat transfer. Heat transfer from a hot object and a cold object depends on 2 things:
(1) the type of material it's traveling through and
(2) the difference between the temperature of the hot object and the cold object.

Let's look at the first factor, the type of material. Heat travels through different objects at different rates, depending on what these objects are made of. When you put soda in the fridge, you are cooling the soda with cold air. That is, heat from the soda must travel from the soda to the air inside the fridge. When you put soda in an ice bath, you are cooling the soda with cold water. That is, heat from the soda must travel from the soda to the cold water. Heat travels through water about 20x faster than through air. Why? Water molecules are closer to each other; air molecules are farther apart. So, the ice bath wins point #1.

Now, let's look at the second factor. Let's say your soda is at room temperature, 70Fahrenheit. The ice bath should be at 32Fahrenheit and fridges are usually set at 40Fahrenheit. The difference in temperature between the soda and the ice bath is 38Fahrenheit. The difference in temperature between the soda and the fridge is 30Fahrenheit. So, the ice bath wins point #2. The ice bath wins both points!

The ice bath is colder than the refrigerator, and it also has a higher heat capacity because it's mostly water, so soaks up heat more quickly than the cold air inside of the refrigerator. The greater the difference in temperature, the faster heat drains out of the soda.

In an ice-bath, there is a mixture of water and ice. In the refrigerator, there is only air and the solid stuff that makes the shelves. Of all the substances - for instance, water, oil, plastics, air - on Earth, water has one of the highest specific heat capacities. This characteristic of water means a few things in real life:
1) When water absorbs heat, it absorbs a lot of heat and keeps the heat very well;
2) When water is cooled down, it takes a lot of heat from the outside for it to reach a certain temperature, which is why boiling water takes a longer time than heating up oil;
3) When hot, water can give a lot of heat to other objects (because hot water retains a lot of heat), and when cold, water can cool other objects down very effectively. This is because the cold water can take a lot of heat away from other objects. By contrast, air cannot absorb a lot of heat and therefore cannot release a lot of heat back into the environment or other objects.

Because of the difference in the ability to absorb (take in) and retain (keep) heat between air and water, the ice-bath with water is much better at quickly cooling objects than the air.

In an ice-bath a soda can is surrounded by liquid water, but in a refrigerator it is surrounded by air. Water is a much better conductor of heat than air, which means that heat moves via conduction from the soda into the water faster than it moves from the soda into the air. This means that the soda in ice-water should cool down faster than a soda in a refrigerator.