Across 1,837 ranked games on patch 16.21 in Master and above, Kai'Sa mains win 51.7% of their games in the bot lane.
Their most common build appears in 82.1% of those games and wins 51.3% of its 1,508 games.
It starts 
two Health Potions and 
Doran's Bow, completes 
Kraken Slayer, 
Guinsoo's Rageblade, 
Terminus and 
Zhonya's Hourglass in that order, and takes 
Berserker's Greaves.
One other build is played often enough in the bot lane to be measured on its own.
In the bot lane, Kai'Sa mains fare best against 
Miss Fortune (won 69.4% of 36 games), 
Twitch (won 73.3% of 15 games) and 
Jhin (won 56.8% of 118 games).
Their hardest matchups, the champions that counter Kai'Sa, are 
Xayah (won 39.8% of 83 games), 
Kalista (won 35.9% of 39 games) and 
Zeri (won 41.1% of 56 games).