Huh, quite a weird oversight they made at Reversal Mountain.
At the part where you team up with Bianca, you are free to go back to the entrance of the mountain, and just like in D/P/Pt the partner stays behind and waits for you to come back, but in the main room rather than the entrance to the cave. Once I was actually back in the previous room, I used Dig to bring me back to the entrance of the cave, except that using Dig brought me to the little raised platform right of those Cyclists, not the real entry of the cave.
Entering the main room of the cave where Bianca is, I get her usual line and such, except she is standing at the entrance in the north of the room, while I am at the south, so she's talking from all across the room, and when she says she'll follow you, she actually won't be following for the most part.
Leaving the main room seems to fix the problem, but going into wild battles doesn't, even though she does aid you in battle, and heal you.
It seems getting closer to her makes her try to get behind you again, and she does anything in her power to do so, including walking through the mountains, through other NPCs, even through LAVA if you're playing White 2. It's quite a sight, and quite an oversight. :P
You should, it is quite funny to try and avoid getting 'caught' by Bianca, or making her run through all kinds of odd areas. I am playing Black 2, so I sadly didn't get her running through lava, but she did enter the water, so I imagine it's possible. :P
It doesn't seem to be on Bulbapedia's list of glitches yet, but I don't have an account or a way to make videos of it, so I won't really bother to add it there myself.
It seems rather pointless anyway that Dig would take you to a random platform if that's the last place where you exited the cave, I didn't have my dedicated Fly HM Slave with me, so it took me further away from my goal rather than make me approach it, kind of counter-productive there, game. :P