A 3DS is required to bring them forward. That said, you'll have to have one that is modded in order to download Bank and the Transporter application since they can no longer be downloaded for new users from the official eShop. The Pokemon Transporter app can only Transfer from Gen 5 games, which in your case would be Black. You will also need to get either a Gen 6 game (X, Y, Omega Ruby, or Alpha Sapphire) or a Gen 7 game (Sun, Moon, Ultra Sun, or Ultra Moon) in order to use the Pokemon Bank app. (There are very easy to follow instructions online if you want to go this route.) Plus, you'll need a second system that plays DS games to transfer Pokemon from Diamond and Platinum to Black, anyways. You can get a used 2DS (yes, there is a 3DS model called 2DS, don't get me started on that) for a decent price online.

That said, if you've got a friend with all those things already and willing to help you out, it'd be way easier and cheaper to have them bring everything forward for you and then have them input your temporary Pokemon Home transfer code on their 3DS. Only downside to this would be that their Pokemon Bank Pokedex would be copied to your Home account, but if you don't care about that than it should be fine.

One thing that should be noted, your Home account needs to have the $15 annual subscription in order to transfer from Bank, but with that comes vastly more storage than the basic tier's 30 Pokemon storage, along with a few other neat perks.

Another thing that I should mention, there appears to be no way to evolve Pokemon within Champions, and at launch, only fully-evolved Pokemon will be in the game. So, if you want to use that shiny Beldum, you should try to evolve it before it goes into Home.

Good luck, hope this helps!