Several abilities or attacks allow you to substitute your Weapon or Ballistic Skill Bonus for degrees of success on an attack, or instance, the Warrior's Expert at Violence or when a target is helpless. Do you use the modified BS or WS for the degrees, or just your base. That is, if I made an attack that was at +30 to my BS of 40, would the degrees of success be 7 or would it be 4?

You would use the base ability bonus as written on your character sheet. Those modofiers give a bonus on a test, but they don't actually change your ability score.

Very few things nowadays will change your actual characteristic. For instance, it used to be the case that power armor gave you a bonus to Strength, which ended up requiring a rules hack to play nice with Unnatural Characteristics functioning as multipliers before BC. But Only War changed that to just have it grant you bonus Unnatural Strength (now an additive bonus), which in practice is notably less likely to produce weird rules interactions like that or like what you were referring to.

That said, there is still at least one thing that gives an explicit bonus to BS. Auto-Senses (Enemies Within) are now an upgrade to a power armor helmet (and thus a mid-game or late-game item), and they explicitly grant +5 to BS when used.