Across 1,614 ranked games on patch 16.21 in Master and above, Draven mains win 54.8% of their games in the bot lane.
Their most common build appears in 41.3% of those games and wins 54.4% of its 666 games.
It starts 
two Health Potions and 
Doran's Bow, completes 
Bloodthirster, 
The Collector, 
Lord Dominik's Regards, 
Infinity Edge and 
Immortal Shieldbow in that order, and takes 
Berserker's Greaves.
Three other builds are played often enough in the bot lane to be measured on their own.
In the bot lane, Draven mains fare best against 
Kalista (won 67.7% of 31 games), 
Ezreal (won 59.4% of 69 games) and 
Kai'Sa (won 59.0% of 61 games).
Their hardest matchups, the champions that counter Draven, are 
Aphelios (won 47.5% of 61 games), 
Caitlyn (won 48.1% of 54 games) and 
Ashe (won 42.1% of 19 games).