As the others said, you need to be on a YBM fare and there needs to be an upgrade available. So if you are able/willing to spend the extra money, then I'd definitely do this by calling Delta and have them walk you through the process. I've done the ATL-DXB route in BE a couple of times and the lie-flat beds on the 777-200ERs are great. But it's pricey to buy a YBM fare; at least 2 or 3 times what you would pay for a T fare. Sometimes you should know that the discounted first tix are actually cheaper. I just flew to PEK and it would have been cheaper to buy a discounted J ticket than an upgradeable Y ticket, except I couldn't because of company regs.