How can I purchase a 12 Month XBOX Live Subscription from the XBOX Live shop with Bitcoins?

Yes it is possible to buy subscriptions from Microsoft with Bitcoins. (Thanks Joris Vanhecke for pointing this out)

From the link:

To add money to your Microsoft account with Bitcoin:

• Sign in to Microsoft account - Billing with your Microsoft account
• Select Payment options > Microsoft account > redeem bitcoin
• Select the amount you want to add, then click Next
• Review the amount of Bitcoin needed and use your digital wallet to complete the transaction within 15 minutes:
  • On your computer – select Pay with Bitcoin and then pay from your Bitcoin wallet on the same device.
  • On your smartphone – scan the QR code displayed on the page to pay from your mobile wallet app.
  • If your wallet is on another device, you can copy the receiving address and BTC amount to the wallet on your device or the Web and then make your purchase.

Some things to keep in mind:

• You cannot buy gift cards or add funds to other accounts with Bitcoin.
• Most Bitcoin transactions should process immediately. If it doesn't, please wait up to two hours for the transaction to complete before contacting support.
• Money added to your Microsoft account using Bitcoin cannot be refunded, so make sure to review your transaction before paying with your digital wallet.
• You can only use Bitcoin to add money to your Microsoft account and then purchase digital goods at select Microsoft online stores. You can’t use Bitcoin to purchase Microsoft products and services directly at this time.
• Support for adding money to a Microsoft account with Bitcoin is not available in all countries and regions.

You can also buy a 12-month subscription via Paypal on the official Microsoft Store Page.