Once you’ve overcome Vicki’s team, head North to the junction, then East and North again and you’ll run across another Ace Trainer who’s babbling about his computer research.

Battle: Ace Trainer Shaye (2040 Poke)
Opponent: Archen Lv 34, Electabuzz Lv 34

Shaye is also threatening- Archen’s Defeatist makes it easy to handle once it’s below half HP, but its typing make that a bit of a hard sell at this point in the game.  Electabuzz is similarly tougher than you might think, both because of its Light Screen move and because of its surprisingly high speed.

Continue past Shaye to the deepest part of the cave and you can turn up a Thunderstone, a useful evolution item for many Electric-type pokemon.

That done, it’s time to return to the second floor where Bianca is.  Head up the stairs to the right of her and you’ll find yourself near a crossing of two paths.  An Ace Trainer waits here, pacing back and forth in search of a fight she can use to show off her team.

Battle: Ace Trainer Mary (2040 Poke)
Opponent: Tirtouga Lv 34, Magmar Lv 34

Beware Mary’s Magmar- the thing’s Special Attack is so high it does considerable damage with its Flame Burst, even to Fire-types (as long as they haven’t got Flash Fire).

East of here is the exit to the cave, but you don’t want to head there just yet.  Instead, go South to find a Hiker guarding an Item Ball.

Battle: Hiker Otto (1024 Poke)
Opponent: Aron Lv 32, Nosepass Lv 32