The range for Misty Step is "Self" which is defined as in the spellcasting section of the rules stating "Other spells, such as the shield spell, affect only you. These spells have a range of self." The "affect only you" would seem to say that anything not you is excluded from this spell. Note that this is a range, not a target. The range of the spell ends where the character ends and the Iron Bands begin.
If the Iron Bands specifically said "if the character is moved, the Iron Bands move with them" then it would be different, but as stated in the item all it does is apply the condition of restrained. This is no different than a net, a grapple, or any condition that allows you to still see and speak the verbal component of the spell.
I admit that this is somewhat open to GM interpretation, but I'd argue that the character casting the spell (and the items listed on their character sheet) get teleported. To do anything else opens up spells with a range of "self" to be extended to other items carried or items that surround the caster.