Having emptied the Strange House of everything of value (and some experience points), return through the grass to the main path.  Heading North past the female Cyclist will allow you to duck left and grab a Full Heal before heading down some stairs to the Reversal Mountain entrance.

Reversal Mountain’s first floor is pretty typical of caves, providing you with Woobat and Boldore, though it also includes Skorupi and, depending on version, either Spoink and Grumpig or Numel and Camerupt.  The pokemon here are levels 31-35, so you shouldn’t have much issue handling them.

Go North up the stairs and take a turn to the left to snag a Max Repel, which could be useful if you find you need to escape to go to a pokemon center and don’t have an Escape Rope handy.  Thankfully, this will quickly become a non-issue.

Resume climbing the stairs and you’ll come to an opening in the wall to your right.  Slip through and you’ll run across Bianca.  The flighty researcher greets you, and then explains that there’s something she’s investigating here.  She points out that the wild pokemon in the area are quite tough, and asks you to accompany her.  This starts a doubles area of the mountain, as Bianca travels with you, healing your pokemon completely at the end of every battle.  Bianca brings three pokemon to the fights, all of them offensively focused- a Musharna with Hypnosis and Psychic/Energy Ball/Shadow Ball combo, an Intimidate Stoutland with the elemental fangs and Return, and a Mienfoo that puts together Fake Out, U-Turn, Drain Punch, and Acrobatics to pull some impressive damage.  Her pokemon are level 40 to boot, so you’re pretty safe around here.

Head East and run into a double battle after a short corridor.

Battle: Backpacker Kumiko and Hiker Jared (2072 Poke)
Opponent (Kumiko): Golbat Lv 37, Darmanitan Lv 37
Opponent (Jared): Boldore Lv 37, Excadrill Lv 37

South of Jared is a PP Up in an Item Ball you should grab, then resume heading East.