The roaming legendaries are pretty hard to catch since they're obviously roaming. The route changes every time you enter a new route, so it's not enough to just look at it on your map and go to that place, you just have to keep going to random places until it happens to be in the same location as you. There are a few things you can do about it. After leaving the Vermilion City Pokémon Fan Club house with Copycat's doll, Latios or Latias will roam Kanto.
You could simply quit trying to go after it and battle it whenever it comes up, just remember that the roaming legendaries will try to flee.
You could use the repel method to get to it rather quickly. Go to a route with a bunch of weak pokemon, make sure it is an area close to the next route. use a repel and run around 15-20 steps with a pokemon at level 34 leading your party. after a few steps, go to the next route, come back and repeat. This repels everything except any roaming legendary over level 34. After about 15-20 minutes, it should hopefully appear. It takes time, but it's faster than blindly walking through routes hoping it will appear. You can also just walk back and forth and check your map each time until it comes up, saving you repels.
You'll probably want something to trap it with, such as mean look, or use your master ball if you still have it.