The bard's Jack of All Trades feature says:

Starting at 2nd level, you can add half your proficiency bonus, rounded own, to any ability check you make that doesn't already include your proficiency bonus.

I was wondering if this meant I added it directly into my abilities (Str:10 + 1) or if I added it to the bonus (Str: 0 + 1)

Or If I had the completely wrong and just added it into the skills themselves (Athletics 0 + 1)?

I was also wondering if later on when I get a proficiency bonus of +4 do I go back and re-adjust the scores because half the proficiency would then be 2?