So last night my warlock leveled, and I took a dip into Bard.  I am referencing this part of the PhB, and just want to be sure I'm understanding this correctly; 

"Pact Magic. If you have both the Spellcasting class
feature and the Pact Magic class feature from the warlock
class, you can use the spell slots you gain from the Pact
Magic feature to cast spells you know or have prepared
from classes with the Spellcasting class feature, and you
can use the spell slots you gain from the Spellcasting
class feature to cast warlock spells you know."

I'm reading this as I have some first level spell slots that I can use to cast Warlock spells.  Does this mean I could case Hex, using a first level spell slot?  Pact magic states you always cast at the highest spell slot, but I wanted to make sure the multi-class rules being more specific.  This means I could cast my level 1 Warlock spells using the spell slots I receive as a Bard.  Is that correct?

You are correct.

In fact, it's a very popular reason for multiclassing a Warlock, to give you a few lower-level spell slots to use with Warlock spells that can't or don't need to scale, like Hex or Faerie Fire