You don't have to remove the bumper to do it. Source, I've changed the fog bulbs 10+ times easily at this point. If you lay in front of the directly in front of the car but biased towards the side the fog light you are replacing is on you can snake your arm up. It will take practice and can be frustrating but I assure you it is far quicker than taking the bumper off. At this point I've replaced both a headlight bulb and a fog bulb in under 10 minutes with the headlight maybe taking 3 minutes of that time at most including testing.
Yes, not really necessary to remove the bumper as there are access covers
at the bottom of the bumper facade just forward of the wheel wells. You need a short
handled screwdriver to unlock and remove the covers.
It is a tight fit, however, to reach inside and remove the bulbs (helps if your hands are
smallish). It may also help to raise the car a little with a jack to ease reaching for
the bulb and connector assembly because of the Accent's low ground clearance.
Also, remember not to touch the glass portions of the replacement bulbs with your bare fingers.
Wear clean disposable rubber gloves or use a clean rag/shop towel to handle the bulbs.
That said, it's a fairly easy DIY procedure...just take your time while doing it.