You need to open it with sudo.
sudo vim ~/.bash_profile
The file appears greyed-out when you show hidden files because Mac OS X displays hidden files as greyed out so you can differentiate them from non-hidden files. You should still be able to edit the permissions on the file (you don't need to, though).
If you want to be able to edit without being root, you can change the owner of the file.
sudo chown your_user_name ~/.bash_profile
