Some of the bugs in Animal Crossing: New Horizons will run away from you when you get to close to them. You want to make sure you capture them, and if they notice you, they will run away. You can catch them by sneaking with your net.
To start sneaking, take your net out of your inventory and hold it. From there, hold down the A button, and your character will lower down into a defensive stance. Whenever you move them forward while in this stance, they will slowly move forward, careful in how they step the entire time when you let go of the A button to lash out with your net, so make sure to be close to the bug when you release the button. You want to use this mechanic whenever you’re attempting to capture some of the tougher bugs found in the game.
You can practice this technique whenever you want to try it. Bugs like the butterfly are extremely easy to capture, so you don’t have to worry about scaring them during the start of the game. Later on, though, you want to use the technique whenever you encounter a new bug you have yet to add to your collection. You don’t have to obsess over it, but it’s good to know to use rather than watching your potential capture fly away from you because you were too eager.
Sneaking bugs is essential, so remember to use some patience when attempting to relocate them to your museum. If you already have them, feel free to sell them to Tommy or Timmy for some additional Bells.