Bob the Fighter takes the Magic Initiate feat and selects hex as his once-per-day spell given by the feat.
Bob later finds a Spell Scroll of hex.
Can Bob use that spell scroll, or not?
To cast a spell from a spell scroll, it must be on your class spell list. Bob does not have hex on his spell list.
If the spell is on your class’s spell list, you can read the scroll and cast its spell
The spell you learn from Magic Initiate is not added to a spell list. It gives you an alternative method to cast spells separate from Spellcasting and similar features.
You learn that [1st-level] spell and can cast it at its lowest level.
As DavidCoffron points out, "to cast a spell from a spell scroll, it must be on your class spell list."
If the spell is on your class’s spell list, you can read the scroll and cast its spell [...] (DMG, pg. 200)
The Magic Initiate feat does not grant a spell list to a non-spellcasting class. It simply provides access to a spell (and two cantrips) from a class's spell list:
From PHB, pg. 168:
Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class's spell list.
In addition, choose one 1st-level spell from that same list. [...]
Nowhere does it say that you have a spell list now, since that's tied to classes; you simply have the cantrips and spell that you pick.
Caveat: This is assuming that Bob the Fighter doesn't choose the Eldritch Knight archetype, since that would give him access to the Wizard's spell list, which is effectively the Eldritch Knight's spell list. Of course, hex is not on the Wizard's spell list, so Magic Initiate still doesn't give you the ability to cast hex from a scroll.