I also encountered this problem (in Linux), but appeared to have found a simple fix.
When the bobber is cast and hits the water the game seems to randomly play either splash.ogg or splash2.ogg from .minecraft/assets/sound/liquid, but when the bobber drops under the water the game attempts to play splash.ogg from .minecraft/assets/sound/random. Unfortunately the 1.6.x installs don't come with a splash.ogg in the random directory so the game is unable to play the sound.
The simple solution for now is to download the correct splash.ogg from http://s3.amazonaws.com/MinecraftResources/sound3/random/splash.ogg (the place 1.5.2 gets it from) and put it into .minecraft/assets/sound/random. You may need to restart Minecraft after doing so, but it should work correctly after.
Jeff L
I also encountered this problem (in Linux), but appeared to have found a simple fix.
When the bobber is cast and hits the water the game seems to randomly play either splash.ogg or splash2.ogg from .minecraft/assets/sound/liquid, but when the bobber drops under the water the game attempts to play splash.ogg from .minecraft/assets/sound/random. Unfortunately the 1.6.x installs don't come with a splash.ogg in the random directory so the game is unable to play the sound.
The simple solution for now is to download the correct splash.ogg from http://s3.amazonaws.com/MinecraftResources/sound3/random/splash.ogg (the place 1.5.2 gets it from) and put it into .minecraft/assets/sound/random. You may need to restart Minecraft after doing so, but it should work correctly after.