BASICS:
1) She always runs away from you, but after some time, she stopps and stays in the area, even when you are there, too.
2) She can't move to Cianwood City, you won't find her in caves, towers, water or cities.
Now, let's try to understand her moves better.
1) She likes the area around Violet City and Ecuteak City. This includes the Routes 31, 32, 36, 37, 38 and 42. The greatest chance to see her is at Route 42 but 38 and 37 are good, too.
2) She loves to play the game "You are slow and I'm not". This means: You are in Violet City and she is at Route 32. You get your bike and go to Route 32. When you arrive, she is at Route 36. So you go back through the city to Route 36 and when you look in the Pok�dex again, she is at Route 32 again. You go there, now angry, and when you are there, she is at Route 31 this time.
This game can continue until you get insane, you fly to another city, or she is nice and stopps. It's annoying!
3) The best chance to meet her is in Ecruteak city. She likes all three Routes around the city, so here are the possibilities when you fly there and she is around you:
a) She is at Route 37, you go there. She'll move now. If she goes to Route 36, you have bad chances. If she moves to Route 38 and she stayes there when you are in the city again, you have a good chance that she'll still be there if you go to the Route now.
b) She's at Route 38 and moves when you are there, too. You have good chances if she moves to Route 37 and a chance of 80% if she is at Route 42. When you are back in the city and she is still on one of the Routes (she'll be in 70% of your tries), you have good chances. If she is at Route 38 again, she playes her game (look above). But most of the time, she is at Route 42 and she stayes there. Maybe the water is in her way, I dunno. This is where you need surf, so make sure you have it!
c) She's already at Route 42. In this case, your chance is at 50% that she stays there when you move to the Route.
d) She is at Route 36. That's more difficult than the others, but it could be worse. Try to bring her to Route 37. If she wents there and then further to Route 38 or 42, look at a)-c) to find the next steps, good job. If she moves to Route 36 again...well, forget it, she likes this game really!
Of course, sometimes you went to a Route and suddenly she is kilometers away and nobody knows how she got there in this short time. But most time, she moves like I said above and you need around 10-15 minutes before you can battle her. If you fly to Ecruteak City or Violet City and she isn't around, justfly to the same city again. I really suggest these two cities because sometimes she is at Route 36 and this Route leads to both citys.
Now I wish you good luck, I hope this helps you a little bit!