Not always true. I am also wearing C cup but my arms are not big. I have some friends who are also having bigger bust but have small arms.

In order to slim down your arms. You can do some do some exercise that focus on your arms

You can refer the link below for arm exercies
http://www.youtube.com/watch?v=2bCXWB9GkGQ

Can try out those exercise that not only slim down but toning your arms too. You can see the difference in 2 weeks time if you continue do those exercise everyday.

Just need to be precise and patient in doing those exercise if you want to slim down faster. Good Luck