Look, the most efficient way is to run around with your net in your inventory, ready to be equipped, and shoo away (or catch and release) any other bug you see...
The fact is that the game can only handle a given amount of bugs in the whole map at one time... So shooing away any other bug really helps!
Also, play with your audio all the way up, or consider using headphones for this task, since the sound of them crawling around is very distinctive and can be heard from quite a distance.
As soon as you spot one, grab your bug net as quickly as possible and enter sneak mode (by keeping the A button pressed while holding the bug net) and get close to them... As soon as they notice your presence, they will stand perfectly still and just hiss at you, as long as you are holding your sneaking position. At that point, just get in range and go for the capture!
My first scorpion fell in the river, too, and on that same day I was bit by my first Tarantula. But with this method I manage to catch AT LEAST 3-4 scorpions/tarantulas each night, if I look for them hard enough!
Good luck and happy hunting!~