The following things are true:
- Bards are allowed to use their musical instruments as spell focuses.
- Proficiency with a musical instrument allows you to add your proficiency bonus to ability checks made with that instrument.
- Using an musical instrument in place of a material component means you are using the instrument to cast the spell.
If a spell has you make an ability check as part of casting the spell and your instrumental focus can be used, does your proficiency bonus from instrument apply to the check?
This is a purely theoretical / fringe theorycrafting situation as I have not found a spell that requires a material component that has the caster make an ability check.
The three spells that I know of that call for ability checks (dispel magic, counterspell, and telekinesis), do not require material components, so as far as I understand it, the instrument focus cannot be used. The spell fabricate specifically targets proficiency with artisan's tools as being used (which is a different question if Jack of All Trades applies, and thus anything can be created...)
But considering the Magical Secrets feature that every bard gets and the College of Lore's Additional Magical Secrets feature, there might be a spell out there that that fits this description.
Could the bard use their instrument focus to apply a proficiency bonus to the ability check?
Alternatively, if a spell that calls for an ability check is cast from a magical instrument (such as an Instrument of the Bards), would the proficiency bonus for being proficient in that instrument apply to the spell's ability check?