Your Win Condition
Secure the extended trade. Your best early timers are level two or level three before she gets access to more abilities. Use Vamp Scepter/Ravenous Hydra to heal back her poke.
General Strategy
Run Doran's Blade with Ghost and Flash. You should actually give her priority early game. If you try to push against her, she can Q-hop away easily, preventing the long trade you need. You need to rush Ravenous Hydra with an early Vamp Scepter.
Trading Patterns
She wants short trades; you want long trades. If she jumps onto you and uses spells to reach you, hit your axe and pop Ghost—it is 'go time'. Use Ghost to run right through her W if necessary. When going for the all-in at level six, throw 'baby Q's' (short range) so they are easy to pick up, even if she uses her hop. You can ult her ultimate ability, but you must ult before her spell hits you.
Wave Management
Be gentle with the wave; let it come to your side. Make sure to trim the wave so she doesn't get a huge level two advantage. Value your base timing highly to heal off her poke (using Vamp/passive) and maintain resources.
Their Win Condition
Short trades. Bel'Veth wins by utilizing her mobility (Q-hop) to prevent you from getting extended trades if you are pushing against her.

