In the Pulp Cthulhu variant of Call of Cthulhu 7e, there are various ways to get bonus dice to skills (notably talents and insane talents).
Do those bonus dice also apply to skill improvement rolls? How do they work there if so?
No, there are no bonus or penalty dice associated with skill improvement rolls.
Think about what it would mean to add a bonus die to a improvement roll. It would actually make it less likely that the given skill would improve. Likewise a "penalty" die would actually make an increase more likely.
Therefore, it doesn't make sense to apply the bonus/penalty die system to the skill improvement roll.