Here is how you beat Kalista

1. Stand next to bush
2. Attack her
3. Step into bush before her counterattack lands
4. You won the trade. Her attacks require vision on you to connect, meaning that if you stick-and-move like this, she cannot reciprocate.

Basically if you are against kalista, you need to start with scanner so you can remove any ward she places in the lane bushes, whether top or bottom lane. Then, you just poke poke poke all day long because she literally cannot do anything about it unless she wants to also stand in the bush next to you, which removes her mobility advantage.

Edit: The best way to look at it is this: Her auto-attacks are like Garen's ult used to be.