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The reason is actually quite simple. The amount of heat required for something to change phases i.e. liquid to gas or liquid to solid depends on a property of the matter called specific heat and its mass.
Note that heat is not actually how hot or cold something is but the actual energy of something so when I say the heat required for something to change phases it can either mean a gain or loss of heat. In the case of freezing water we will be talking about a loss of heat.
Now onto the equation:
Q = cmdT
Q is the variable for heat measured in joules
c is the variable for specific heat measured in joules/gram
m is the variable for mass measured in grams
dT is the quantity of the change in temperature
This particular equation does not actually represent the amount of heat needed for matter to change phases. To find that we use another equation and a property called either the Latent Heat of Fusion (liquid changing into water or vice versa) and the Latent Heat of Vaporization (liquid into gas or vice versa). That equation as well depends on the mass of the matter and I can't remember it off the top of my head and my physics book is not handy but its bascially along the same lines as Q = cmdT except it has a new property called the heat of fusion factored in. The basic idea you need to know is that the amount of heat required depends upon its mass.
As you can see the amount of heat needed to for something to change phases is directly proportional to its mass. Therefore if you have more some something, in the case a more water in a bottle, it will require a different amount of heat to change phases.
In other words, the more water you have, the more energy it will need to lose in order to freeze.
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