After you reach Lentimas Town with Professor Juniper, Bianca leaves to visit Reversal Mountain. You should go there, too.
The Path to Reversal Mountain
Just after you exit Lentimas Town, you see a Cyclist going around. He's Cyclist Jeremiah. He sends out a level 37 Zebstrika.
East from him, there Cyclist Adelaide, who has a level 37 Unfezant.
If you continue going through the dark grass to the east, you find a Strange House. It's an optional place where you can get items and fight trainers. If you go there, be sure to use your Dowsing Machine outside of it to find TM30 Shadow Ball.
If you go north from Cyclist Adelaide, you find the stairs leading down to Reversal Mountain, but before that, there is a Full Heal just south of the stairs.
Go into Reversal Mountain.
Inside Reversal Mountain
If you are playing Black 2, Reversal Mountain is watery inside, but if you are playing White 2, Reversal Mountain has lava inside. The layout is slightly different between the two games.
Go north from the entrance and then left. There's a Max Repel there. From there, go east again, then north. Go into the cave opening.
Here you find Bianca. She's having a tough time getting past the pokémon in here and asks you to join her. She'll heal up your pokémon after every battle.
The two main things to do in Reversal Mountain are to find Heatran's cave and to find the exit to Undella Town. First, let's go to Heatran's Cave.
Find Heatran's Cave
If you're playing White 2, go east to get a Hyper Potion.
Now go south. In Black 2, you'll encounter Black Belt Corey here. He does a Rotation Battle with a level 37 Gurdurr and two level 37 Scraggys. Go east from Corey to find a Nugget. Go south from him and use your Dowsing Machine to find a Green Shard on a stalagmite.
In White 2, you can go east to encounter Battle Girl Chan. She fights a Triple Battle using two level 37 Riolu on the outside, and a level 37 Gurdurr. Use your Dowsing Machine near the Battle Girl to find a hidden Elixir. Then go north and east from her to find a Hyper Potion. There is also a hidden Star Piece near her.
In both games, you'll encounter Backpacker Kiyo and Hunter Markus to the south (they are west and south of Battle Girl Chan in White 2). You can fight each one individually if you talk to one of them from the side (to do this in Black 2, talk to Kiyo from above; to do this in White 2, go south from Battle Girl Chan, then west, then north and talk to Kiyo or Markus from below) or you can fight a double battle with them if you walk between them. Kiyo has a level 37 Golbat and a level 37 Swanna, while Markus has a level 37 Gurdurr and a level 37 Crustle.
Go into the tunnel east of the Backpacker and Hiker. In Black 2, you find a Hyper Potion there, and if you use your Dowsing Machine, you find a Blue Shard. In White 2, you find TM69 Rock Polish in this tunnel.
Go west from the tunnel, then go south. There is a cave door. If you go in, there are a couple of paths leading outside, where you can get a Smoke Ball and an Escape Rope.
Back inside, go east. In Black 2, you encounter PKMN Ranger Eliza, who has a level 38 Banette and a level 38 Golduck. Eliza gives you a Persim Berry when you win. In White 2, you encounter PKMN Ranger Lewis, who has a level 38 Watchog and a Level 38 Camerupt. He gives you a Rawst Berry when you win.
East from the PKMN Ranger, Bianca will ask to check out the cave entrance up above. First, battle Doctor Derek, who is standing just outside of this cave entrance. He has a level 38 Swoobat. Derek heals you up after the battle.
Go into the cave. This is Heatran's cave. Go up to the middle of the cave and Bianca will say that it feels strange here. She wonders if this is Heatran's Lair, where Reversal Mountain first began. Go back outside.
Go to Undella
Now that you have helped Bianca find Heatran's cave, it's time to find the exit of the cave that takes you to Undella Town. The layout of the cave in this area is very different between Black 2 and White 2, so the sections below are separate for the two games.
In Black 2, go east from Doctor Derek then north when the path splits. This tunnel has TM69 Rock Polish. Go east from there to encounter Battle Girl Chan. She fights a Triple Battle using two level 37 Riolu on the outside, and a level 37 Gurdurr. Go north from Chan to find a Revive. Go east from her and use your Dowsing Machine to find a Star Piece.
After exploring the cave east of Doctor Derek, go all the way back to where you first met Bianca. From there, go east to find Backpacker Kumiko and Hiker Jared. You'll have to fight a double battle with them. Kumiko has a level 37 Golbat and a level 37 Darmanitan. Jared has a level 37 Boldore and a level 37 Excadrill. Go south from Jared to find a PP Up.
Go east from Kumiko and Jared to find a couple of Ace Trainers. They are Ace Trainer Ray, with a level 39 Vibrava and a level 39 Camerupt, and Ace Trainer Cora, with a level 39 Grumpig and a level 39 Drifblim. South of the Ace Trainers, use your Dowsing Machine to find a hidden Calcium.
Go east from Doctor Derek. Continue all the way east and use your Dowsing Machine to find a Red Shard. Now go back to the west. Go past the first north tunnel and go up the second north tunnel. Up here you encounter Black Belt Corey. He does a Rotation Battle with a level 37 Gurdurr and two level 37 Scraggys. Use your Dowsing Machine here to find a Star Piece.
Go down the stairs to find a Flame Orb, then go up and west. There is PKMN Ranger Eliza. She has a level 38 Krokorok and a level 38 Arcanine. She gives you a Rawst Berry when you win. Use the Dowsing Machine near her to find a Fire Gem. Go back upstairs.
Go north, then west. There is a PP Up here. Go east, past the path that you just came from, and go south to find Hiker Kumiko and Backpacker Jared. Kumiko has a level 37 Golbat and a level 37 Darmanitan. Jared has a level 37 Boldore and a level 37 Excadrill. Get the Revive near Kumiko and Jared.
Go north from Kumiko and Jared to find a couple of Ace Trainers. They are Ace Trainer Ray, with a level 39 Vibrava and a level 39 Camerupt, and Ace Trainer Cora, with a level 39 Grumpig and a level 39 Drifblim. You can go west from them and use your Dowsing Machine to find a hidden Calcium. There is also a hidden Yellow Shard in the tunnel south of the Ace Trainers.
The rest of the cave is pretty similar at this point. Just go east from the Ace Trainers. The scientist here doesn't battle you. He will give you TM54 False Swipe. In White 2, go south of him to find a Nugget. In Black 2, use your Dowsing Machine to find an Elixir south of him.
In Black 2, go south from the scientist to reach some stairs leading down. Use your Dowsing Machine in this cave to find a Water Gem. Farther in this cave, there is PKMN Ranger Lewis, who has a level 38 Watchog and a level 38 Grumpig. He gives you a Persim Berry when you win. There is a Toxic Orb near him. Go back upstairs and go north to the scientist.
Now go east and into the cave opening, then go south and you can exit the cave if you're ready. You'll end up in Undella Town.