Cass TOTALLY isn't a lane bully.

Okay, I'm a criminal here. I don't like losing, and for the most part, I play champions that absolutely dominate (at low elo, at least; by playing ridiculously OP champions I managed to bring my winrate from absolute crap(below 20%) to almost 45%).

As in; Rek'Sai, Cassiopeia, Udyr, Elise, Fizz, Katarina, Malzahar, Quinn, Xin, etc...

But the biggest lane bully among those is Cassiopeia at my MMR, which is bronze 4-2, for the most part, and is a good mix of intelligent players, and partially people that are quite idiotic. Casseiopeia has no mana problems, insane sustain, insane damage, insanely low cooldowns, and beyond this, has a two-second stun. A two second stun that gives her enough time to kill just about anyone in the game. Her level 2 and 3 damage are enough to make a pre-nerf Lucian cry and a Dr. Mundo with an active ult cry for hacks. Asides from that, if you have any idea what you're doing, you have DOUBLE Deathcap passive, making for about 600 more AP than what your item's numbers are (at the least; a Rabadon's with 500 stacks provides 230-ish AP (don't quote me on that; I'm not sure I have the right numbers.)). I've taken the build:

Seraph's Embrace Rabadon's Deathcap Zhonya's Hourglass Rod of Ages Sorcerer's Boots Will of the Ancients (Always call it Wrath of the Ancients... Ancients are gods, right?)

And about 50 AP from runes. That generally ends at about 1200-1300 AP.

She has boots. Not a single other champion can hit 1000 AP without a fully stacked Mejai's or no boots. Cassiopeia can do this with boots and no Mejai's.

So her lategame is insane, she does more damage than any Marksman in the game, she can solo Baron Nashor (Don't believe me? Go try Cassiopeia out with that exact build, whatever order you want. Get full build and 500 stacks and then go have your team worship snake gods after you get them baron (although you need blue.))

In lane, she can do 200 damage (before MR) every half second. So a good 200 damage per second. At the least. Without counting your Q or W's poison, or ignite. Plus, her Q gives a speed buff and her W applies a slow to anyone in the poison.

Did I mention Furor's procs on her E, making her a kiting MACHINE?

TL;DR: Cassiopeia has more mana sustain, health sustain, damage, lack-of-cooldown, scaling, defense, AP, kiting, and objective control than any other mage in the game, beats most AD-based carries in all of these and beats the rest in most, and lastly, you give her a peel-heavy team (Ashe marksman? Leona support? Shen top? Elise... Anywhere? Anyone with a unit or two of CC combined with a stun destroys.)

Oh, did I mention the Casle combo? Cassiopeia and Rumble make for one of the most insane duo-queue wombo combos in the game.