Bianca gives you HM 02 Fly after the battle. Fly is probably the most useful HM in the game. It allows you to instantly transport to any city or town you have already visited. In battle, the Pokemon flys up into the sky where it is unable to be hit by most attacks during the first turn, then it deals damage the second turn. Go west to cross the bridge and continue north through the grass to find a Scientist. All of the Scientists on this route use X items to increase one of their Deerling's stats during the first turn of battle.
There is an Elixir in the grass near the Scientist. The big building here is the Season Research Lab. There is a Scientist inside that will give you a Leaf Stone if you show him all four forms of Deerling. Deerling has a different form for each season. There is a Hyper Potion to the west of the lab. Continue west along the path to battle a female Scientist.
Keep going west across the fourth bridge to find what looks like an item. If you inspect it, you will find out that it is actually a Foongus. This sneaky Pokemon looks just like a Poke Ball from above. Knock it out or catch it and then battle the Parasol Lady. She has a Frillish. It is Water and Ghost-type so it won't be affected by Normal attacks and it has quite a few resistances.
The first item west of her is a Leaf Stone. You can use it to evolve a Pansage, Cottonee, or Petilil if you want. The item southwest of the Leaf Stone is another Foongus. There is a Pokemon Ranger walking nearby to battle.
He will give you a Cheri Berry after you defeat him. Walk north to cross the fifth bridge and enter the house to the east. Talk to the little girl inside and she will give you a Shiny Stone. You can use it to evolve a Minccino. You can also heal your Pokemon by talking to the lady at the table. Exit the house and walk north to Chargestone Cave. Walk up to the yellow spider web and inspect it. Clay will appear and get his Krokorok to remove the web. He also gives you TM 78 Bulldoze. It does damage and lowers your opponent's speed. Clay will leave so now you can enter Chargestone Cave.