The easiest way to see which Pokémon are close to your current location in Pokémon GO is by checking the Nearby tracker in the bottom-right of your screen. At least this was the easiest way up until a few days ago. Initially, the Pokémon in the Nearby screen would be marked with between zero and three footprint icons—the more footprints, the further away a Pokémon is from your location. Pokémon with zero footprints should be visible to you.
Now, thanks to a bug that everyone is calling the three-step glitch, every Pokémon in the Nearby screen is showing up with three footprints regardless of its proximity.
The Nearby menu still sort of works, however. Whichever Pokémon is in the first spot on the menu is the one that is closest to you. So you'll at least be able to determine if you're going the wrong direction if a Pokémon other than the one you're tracking leapfrogs your bounty in the list. Still, it's possible that you're just moving further away from all of the Pokémon in the Nearby menu, so it's really not ideal.
The issue appears to be related to the Google Maps API, so at least it's not Niantic scheming to make you purchase more Incense. But the sooner they fix this, the better, because tracking Pokémon is way more work than it needs to be right now.