Bards get the ability "Jack of All Trades" which reads:
Starting at 2nd level, you can add half your proficiency
bonus, rounded down, to any ability check you make that doesn't already include your proficiency bonus.
Since your initiative roll is based purely on your dexterity, and it says "ability check" and not "skill check", does that mean that a Bard, starting at 2nd level, will tend to have better initiative than others?
Best Answer
Yes, the Bard adds 1/2 proficiency to initiative.
In 5e all checks are ability checks. This is why every check in published materials is listed as Ability (Name), such as Strength (Athletics).
Initiative is a Dexterity check. Under Initiative in the PHB:
If you can add an ability modifier to a roll, it's an ability check (A saving throw or an attack is a separate kind of d20 roll). If you have a Skill related to that Ability, and you are proficient in that skill, you add your proficiency bonus.
Initiative is a Dexterity check with no other Skill attached to it. Things that modify Dexterity checks work. Other things modify your ability checks as well - such as adding all or half of your proficiency bonus. The Bard has one example of this.
The Champion Fighter's L7 feature has another:
Since Initiative is an ability check that uses your Dexterity, the Champion Fighter also gets half their proficiency to added to their initiative roll.