The first bottle you should get is at Lon Lon Ranch. Go to Lon Lon Ranch during the daytime and enter Talon's House. Talk to him, he'll ask if you want to play a Super Cucco Findin' Game. Say yes, if you can find all three "super cuccos" you will get a bottle of Lon Lon Milk (you can put anything in the bottle after you drink the milk).
A strategy you can use to "legally cheat" is to throw all of the regular cuccos behind the table that Talon is leaning on before you start the game. That way the super cuccos will be the only three cuccos in the room.