and I were discussing whether or not Bardic Inspiration could be used to assist in a Dispel Magic roll.

I think no, since the ability check is a component of the spell, like an attack is a component of Green Flame Blade not an attack action Bardic Inspiration can assist the ability check inside Dispel Magic. Bardic Inspiration is intentionally generous about being able to benefit ability checks of any sort.

— Jeremy Crawford (@JeremyECrawford) April 26, 2021