So, you've decided to be a dragon slayer. There are less convoluted ways of assisted suicide. However, if you aren't here to end it all and genuinely think you will be hailed as a hero, well, you won't be. Why?
1. Dragon avoids direct confrontation
The plural form isn't necessary as we only know about one dragon. This one steers clear of larger units, attacking defenseless supply lines and snatching the nibbles. You can simply survive him by not backing him into a corner, but you won't get far without those snack.
2. The dragon causes the least number of casualties among dragon slayers
Most actually starve to death, go AWOL or get murdered by naruto-running titan zombies that come out during night. Most of that is on the insane leaders here, "friendly fire" is also a common cause of death. This brings us to
3. Anti-dragon rifles are very effective, but you'll never get to use them
The .50 Barret rifle can most definitely injure and kill a dragon (I never tried it, but if it can beat an engine block...), problem is the dragon has time and time again spotted the sniper, hid himself and gave the sniper a leg day by flying to an elevated position. Had to call off the mission because it was about to get dark.
To summarize, we have a creature that read Sun Tzu's The Art of War, has insane mobility (flight) and is pretty fast and nimble in general. He also has the ability to hide himself really well. The dragon is around the size of a large horse, but can somehow squeeze through much smaller spaces. His hide protects against everything up to a .50 BMG.
He can go on for long without food, as long as he isn't using active flight, maybe half of what crocodiles are capable of.
So, this is a battle of attrition right now, and the dragon is winning. How could we catch this dragon without throwing out lots of resources?
Tech is medieval, but with modern-day firearms, but no vehicles, the infrastructure is also inadequate for producing ammo in larger quantities.