Pretty sure the water would take longer to cool from the bottom up

Exactly what I was thinking, what is so bad about just standing it up and freezing the bottom

i think i know what im talking about

A lot of these bottles have built in straws, if there was a block of ice at the bottom you wouldn't be able to use it at all. (since the straw would be trapped in the ice).
Alternatively laying it on its side creates a bigger surface area on the ice, cooling the beverage faster.