I'd break this issue down in two:
- The application process
- The work itself once you're hired
In terms of the application process, it's all about preparation and about your personal and intellectual skills showcasing appropriately during the interviews. That all comes down to preparation.
In terms of the work itself, this might be a bit of a struggle initially, especially if you're mostly used to repetitive/routine tasks. Things will be moving at a much faster pace, the expectations will be much higher and those around you will likely also be performing at a higher level. The bias (from a recruiter's standpoint) will be: can this person, who is definitely smart but mostly used to performing "boring/routine" tasks deliver what we're expecting of him/her?
Due to this last point, I'd summarize saying: coming from internal consulting, the key point you'll want to prove to MBB recruiters is that you are able to deliver under high-pressure and fast-changing environments, giving concrete past examples. This will directly address their potential bias towards you.
Hope it helps.