Bumper will not rust.
Personally, I would not worry about it, however . . .
If the aesthetic bothers you, then there are options ranging $50 to $1,500 dollars.
$50 dollar option is something like ChipEx, which is DIY and works pretty good to hide and protect. If I were compelled to address your defect, I would go with this option.
We tested the product and run a Chipex review. See the results of 3 different cars using the Chipex product. We tyre repairing stonechips.
$1,500 option is professional job where they remove bumper, sand down defect, repaint defect, then apply clear coat to entire bumper for 'new' appearance. Overkill for the defect you present, unless you want your bumper to regain 'new' appearance and cost no objective.
In-between, you could have professional perform their version of a spot-fix, which will equate to them performing something similar to a ChipEx - if not actually using ChipEx with up charge for time/labor. Cost and aesthetic outcome will fall somewhere in-between the first two options presented. Estimated price $250-500.
Given the defect, the first and third options presented will both produce something very close to 'new' appearance. From this perspective, it comes down to your comfort level with DYI versus having a professional perform the job.