Your well established tank will already have colonies of BB to deal with the load on that tank. If you throw other media in there there's no real need for more BB to grow because their numbers won't need to increase unless you add more fish to up the load. Yes, you may get some growing but it will take time and even then there's no guarantee that your newly seeded media will have enough BB on to give you an instant cycle on your new tank.
You could do as your suggesting and when you transfer the media over to your new set up you could also add some bottled BB to help you even more.