Pantheon
Even though he is one of the best roaming mid-lane champions in LoL, his roaming is set up by killing the enemy and freeing himself for roams, after pushing the wave under turret.
This is achievable due to Pantheon's early-game scaling, and a point-and-click stun. Coupled with his passive stacking, he's got enough burst to kill squishy mid laners even before level 3.
Annie
For the same reason she is one of the best LoL champions for beginners, Annie is also a mid lane bully champion. It all comes down to her Q, and her passive stacks.
When killing an enemy unit with her Q, it refunds her mana, giving her a lot of sustain in lane, while also stacking up her passive for free. With four basic abilities cast, her next offensive ability stuns enemies.
This means she can farm for free, freeing up her mana for poke, while setting up for an all-in with her ultimate.
LeBlanc
Even though she's known as one of the worst champions in the game to farm with, LebLanc is still a feared champion in the mid-lane, with a high ban rate. This is because she farms champions instead.
Her kit allows her to be one of the best burst mages in LoL, while also having a lot of survivability. Thus, she can chunk any enemy and force them out of lane, while they can do nothing in return.
If the enemy stays, they can't farm and will die as well. If they leave, they lose farm again, which is one of the foundational strategies of playing League of Legends, and LeBlanc can take a trip to the top lane, to bully another lane too.
Katarina
Katarina is one of the best champions for kills in LoL, as she needs only one trip to the bot lane to get her advantage, to completely dominate the mid lane.
When her kit is used in the right hands, she can dominate the entire enemy team, with constant resets of her abilities. This, in turn, makes her an incredible lane bully, who can't be afforded an inch of advantage, lest she takes over the rift.
Tristana
Over the years, marksmen have found themselves primarily in the bot lane, ADC role, and few can thrive in the mid lane the way Tristana can even today. However, her aggressive playstyle is made for the mid-lane.
As a ranged champion, during the laning phase, she can harass the enemy champions easily. Unlike most ranged champions, she only needs to get to level 3 before her all-in is enough to kill enemies even in a lane as short as mid-lane, not giving them time to escape.
Fizz
Assassin champions are used to coming out from the shadows in team fights to kill their enemies and displaying flashy combos to outplay them. The former can't be done in lane, and the latter usually needs some ability haste items to pull off.
Fizz's intargetability, the ability that makes him one of the best juke champions in LoL, however, allows him to engage enemies straightforwardly, and use a single rotation of his ability, alongside the Electrocute rune, to one-shot the enemy even with only components of his first item.
Zed
Of all the bully melee champions mid-lane has, Zed is the champion with the highest ban rate in the game. And that's for a reason, as his shadows allow him to execute all manner of combos, most of which can't easily be predicted.
By positioning his shadows in a good place, Zed can proc Electrocute with only his shurikens, and chunk the enemy in preparation for an all-in, all from a distance, unlike Fizz who must enter melee range.
The possibilities of his combos are endless, and each and every one spells doom for the enemy!
Malzahar
By far, the most annoying mid-laner to play against is Malzahar. With a decent range of his auto attacks, he can harass any melee mid laner, while his passive gives him a spell shield, forcing every champion to waste one ability to remove it.
Furthermore, the reason that makes him one of the best mid-lane weaveclear champions, also makes him an incredible bully. By summoning his voidlings, he can transfer his DoT to an enemy champion just by the enemy coming near minions to try and farm.
Add to that his ultimate, which forces all carries to buy a cleanse item and waste an item slot, if they want to play the game at all, and you get a simple-to-play mid-lane bully that will force your enemies to rip their hair out in frustration!