Can you really not destroy bots with her? It's pretty simple and straightforward.
Just Q a enemy champion or nearby minion to get some damage on at least 1 enemy champion, wait out the cooldown then use your Q again, follow it up with a E behind the enemy you used your Q on, Press W when you are withing pickup range of the dagger that dropped from your Q, then press R and watch as everything around you either dies or gets real low.
Then any time anything dies you basically get all your cooldowns reset (except for your R, that requires multiple kills) so just continue to use your Q on enemies, drop W's everywhere, and use your E to jump either to enemies or your daggers from your Q's and W', if you get 3 kills you get another use of your ult so you should be able to use it twice in 1 team fight.
If you have any item actives that deal damage don't forget to use them when you can. Hextech Gunblade is a useful item for her.
Just be mindfull of enemy CC, that is your one true weakness, if you get CC'd you die.
Against human players you'll have to be more careful of course, not just due to the CC but also because of all the normal damage they can put out if they focus you and be weary of supports with exhaust. You kinda want your team to go in first and put some early damage on the enemy and spent their CC before you start your reign of terror in their midst and deal some crazy area damage to everything and get continues resets from kills.
The only "tricky" thing is her Q drop point. It always drops some set distance behind the first target that you hit with it.
Her E also gets reset if you pick up a dagger.
You should be able to absolutely destroy bots 1v5 with her, depending on their CC.
