When you exit from the gym, you will get a call from the Xtransceiver. It's Bianca, and she says that she would like to battle with you. She is waiting in the entrance to Route 4. She has received some training from Iris, so don't underestimate her this time. She really has improved a lot!
Bianca starts with Herdier. Herdier knows Take Down and Bite. Since Herdier is a Normal-type pokémon and since Fighting pokémon are strong against Dark moves, Timburr, Throh, and Sawk would be good choices for your first slot.
Her next pokémon is one of the elemental monkeys. It's whichever monkey your starter is weak to. This will be either Pansear, Pansage, or Panpour. This means that if you use the pokémon that you used against the trio in Striaton City, you will do well.
After that, Bianca will send out her starter, which evolved to its second form. This will be Pignite, Servine, or Dewott. Your own starter will probably be a match for it.
Finally, Bianca sends out her Munna. Munna's moves are Yawn, Moonlight, Imprison, and Psybeam. One thing about Bianca's Munna is that it knows Moonlight, which will restore at least 1/4 of its HP. If the weather is Sunny, Munna will be able to restore 2/3 HP with each use of Moonlight. Fortunately, Munna only has 5 PP to use this move, so it won't slow things down too much. Munna also knows Imprison, which means that if you bring a Pokémon that uses any of her moves, your pokémon won't be able to use those moves. Purrloin might be the ideal pokémon to use against Bianca's Munna, because Psybeam won't affect Purrloin, and Purrloin should know at least Pursuit by this time.
Once you defeat Bianca, she will be happy about all of the experiences that she has had so far, and will depart.
Now you can head north to Route 4. There is deep sand just to the left of the road where you can walk around and have pokémon encounters. Darumaka is here, as is Sandile and Scraggy. In this area to the left of the road, you can find a house where a woman with a Sandile will heal up your pokémon for free.
You will also find Cheren. As soon as you walk up to him, he will challenge you to a battle. Beware: in Route 4, since a Sandstorm is going on, your pokémon will be damaged on each turn by the sandstorm, unless it is a Rock, Ground, or Steel pokémon. However, the opponent pokémon will also take damage, unless it is one of those types.
Cheren's first pokémon is Pidove. Pidove's attacks are Quick Attack and Air Cutter. Roggenrola will be a good opponent because it is strong against the Normal attack, and its Rock moves will be strong against Pidove.
Cheren's next pokémon is the elemental monkey that is the same type as your starter. This could be Pansage, Panpour, or Pansear. For Pansage, Sewaddle, Pidove, or Darumaka will do; for Panpour, Cottonee or Petilil or Blitzle will work; and for Pansear, Roggenrola, Tympole, or Sandile will work. If you have the elemental monkeys, though, then you can just use the opposing one.
After the elemental monkey is Cheren's starter. This will be Pignite, Servine, or Dewott. Again, you can use the elemental monkey or the applicable possibilities from the paragraph above to fight against this one.
Finally, Cheren sends out a Liepard. A fighting type is a good choice here, so go for Throh, Sawk, or Timburr.
After the battle, Professor Juniper will call on the Xtransceiver. She'll say that she tried to include Bianca in the call, but Bianca didn't answer. The professor will say that she is waiting for you at the gate to Nimbasa City. Cheren will go on ahead.
Now you're free to explore this area. It's pretty vast, so take your time. Be sure to have your Dowsing Machine active, because there are many hidden items around here.
You can start by exploring the area that you can reach to the left of the exit to Castelia City. There is deep sand here, where you can encounter Scraggy, Sandile, and Darumaka (you will encounter these three all throughout Route 4.)
After you have explored that area, you can go north to reach a sandy area. Above it, you will find a road that goes toward the left. If you follow it to the left, there is a worker who will battle you, and there is a small house where one of the two workers will give you the TM for Dig. North of this house, you can reach the entrance to Desert Resort, which is a large area with a constant sandstorm, and there is an entrance to some ruins there.
If you take the northward path that is to the right of the one leading to Desert Resort, you will reach the entrance to Nimbasa City.
The trainers on Route 4 include a couple of fishermen who have Basculin, a Parasol Lady who has two Tympole, Workers who have Roggenrola and Timburr, and several backpackers who have various different pokémon.
There are also plenty of items around here, both hidden and visible. These include the TM for Torment, a Pearl, an Ultra Ball, a Hyper Potion, and more.
The Desert Resort is optional, but you might as well go for it because you can get a lot of experience there, and you can catch quite a few new pokémon, which will be a big help in preparing you for Nimbasa City.