iTunes billing for Netflix is currently only available by opening a new Netflix account through your Apple TV. If you choose to be billed through iTunes, the iTunes store will automatically bill you each month for your Netflix membership once your free trial ends. Memberships started through Apple TV function just like a regular Netflix account — you can stream on your computer or any other Netflix ready device.
If you want to use your Netflix account on other Netflix ready devices, you will first need to set a Netflix password. Go to https://signup.netflix.com/loginhelp to create a Netflix password and begin watching on other devices.
Navigate to the Your Account page on the Netflix website and look for the Apple logo with the statement "Your Netflix membership is billed through iTunes" to verify your account is being billed through iTunes.
To learn how to update your iTunes method of payment or other iTunes account details, see Apple's support article at http://support.apple.com/kb/HT1918
You can use an iTunes gift card to pay for Netflix as long as the gift card is applied to the same iTunes account you used to sign up for Netflix.
If you are being billed through iTunes and have any questions regarding billing, contact Apple Care using Apple's Express Lane: http://www.apple.com/support/appletv/contact/3rd-party-subscriptions/
You will need to use iTunes to cancel iTunes billing for your Netflix account, and restart your membership from the Your Account page on the Netflix website. For detailed instructions on using iTunes on your Mac or Windows computer to manage your subscription, see Apple's support article at http://support.apple.com/kb/HT4098.