From www.seat61.com.
Don't bother trying to use the German Railways (DB) website www.bahn.com to buy a Deutschland ticket as it only accepts payment by direct debit and setting up a direct debit with a non-German bank account results in an error message.
The easiest way for foreign visitors to buy a Deutschland ticket is to buy from Bremen area transit authority VBN using their FahrPlaner app because (a) it accepts payment by credit card, (b) it's in English, and (c) it has no problem with overseas users, overseas addresses or UK postcodes.
Step 1, download the FahrPlaner app for iPhone or MFahrPlaner app for Android (please let me know if those links stop working).
Step 2, the app should open in English. Click the menu icon top left and go to Tickets. Then select Deutschlandticket.
Step 3, click the red PROCEED TO LOGIN button at the bottom. Then click Sign up for free and register, it lists most countries including United Kingdom and United States and has no problem with UK postcodes.
Step 4, select Credit Card and buy your Deutschland ticket.
This is a rolling subscription which you can cancel at any time.
You show the Deutschland Ticket as a QR code in the app on your phone. Easy!
If you only want one Deutschland ticket for one month, buy it before the 10th of the month then cancel your subscription also before the 10th of the month. That prevents payment being taken for the following month.
To cancel the subscription, you must open the order confirmation email they sent you when you bought it and click on the cancellation link. You cannot cancel your subscription from the app.
If you have children, you'll need to use the RMVgo app instead, see the paragraph about children above.