Ninjask
Ninjask is the fastest Bug-type Pokemon to date, outspeeding even Mega Evolutions with it's insane 160 base Speed.
Golisopod
The Bug type with the highest BST is Golisopod, with a 530 BST. In-game, you'll want to go hyper-offensive, so here's a set:
Golisopod (any item)
Ability: Emergency Exit
Natures and EVs don't matter
-First Impression
-Leech Life
-Liquidation
-Iron Head
If you're including the IOA, then Volcarona has the highest BST, at 550.
Volcarona (any item)
Ability: Flame Body
Natures and EVs don't matter
-Quiver Dance
-Fiery Dance
-Bug Buzz
-Giga Drain/Psychic
With the CT now released, Pheromosa has the highest BST at 570.
Pheromosa @ Any Item
Ability: Beast Boost
-Lunge
-High Jump Kick
-Poison Jab
-Drill Run
Centiskorch
The Bug type introduced in Galar with the highest BST is Centiskorch, at 525.
Centiskorch (any item)
Any ability, I would recommend Flash Fire
Natures and EVs don't matter
-Coil
-Fire Lash
-Lunge/Leech Life
-Crunch/Thunder Fang