Walkthrough: (Source: Experience) If following this doesn't help then let me know exactly what step the issue arises at.
First, start up Pokemon Black 2. Place any Pokemon you wish to transfer into Box 1 (it will automatically transfer the whole box).
Second, close Black 2 go to the home screen. Make sure the icon for Pokemon Black 2 is showing (in the place that the inserted game card shows up). If it is not, there may be an issue with your cartridge. If it is, continue.
Third, open Poke Transporter. As long as the Icon for Pokemon Black 2 was visible on the home screen, it should automatically recognise the game and connect you to your Nintendo WiFi account and the PokeBank servers. It will load up the first Box from Black 2 and ask you to confirm sending the Box over. Note: At this point it runs a scan on your Pokemon for any illegal Pokemon (i.e. Pokemon caught in a Cherish Ball, Pokemon with wrong moves, Pokemon with wrong abilities, or Pokemon without a legitimate PID in general). Any of these it will leave in Pokemon Black's Box.
Fourth: After confirming, it will transfer your Pokemon to the PokeBank Transfer Box and return you to the start screen. Return to the DS home screen, eject Black 2 and insert X. Open up PokeBank.
Lastly: Navigate to the PokeBank's Transfer Box (one left from the starting box) and your Pokemon will be there.