Can a character escape the Iron Bands of Bilarro (DMG p. 177, listed in the SRD as the Iron Bands of Binding) with the misty step spell? To clarify, I am not asking if the bands prevent teleportation. I am asking whether the bands are teleported with the character as he teleports using misty step.
The Bands do not prevent teleportation
The limitations of Misty Step are clear:
you teleport up to 30 feet to an unoccupied space that you can see
The only way the Iron Band could interfere with any of these if it obstructed the target's vision. There is no trace of this in the description.
The Bands might teleport with you
In your opinion, could a wizard that's tied up (but not gagged) cast Misty Step to free himself?
It's up to the DM. I'd say you could teleport out of bonds that are fixed to a wall or the like.
Misty Step is magic, and you pay the price, spend a spell slot and an action. You can clearly get out of a grapple with Misty Step, and shackles seem even simpler things. Once the Bands caught you, they are no different from shackles.
So I would let Misty Step get you out of it.