Well the goal of solo-bot lane is of course:
get farm / gold and deny it from the enemy carry.
thus all champs who can scare the adc and sup back are quite good picks.
always crucial to this is, that you have vision of possible ganks and the brush(to counter getting zoned).
not too gold dependent
you will also have to care about your range for effective farming/harrassing,
thus you'd either want a champ to have some ranged ability/autohit or a champ with a low-cd gap-closer/escape to prevent losing too much hp after getting farm.
Range or gap-close/escape
you should get used to the thought, that you will not get any ganks, but there should be ganks by your jungler. to effectively lock down your enemies you could use some hard CC
All the mentioned points are a "nice to have" and not all necessary
i would suggest either Elise, Riven, Panth or Nidalee
Elise: can be played tanky and has good harrass, as well as cc and a nice gap-closer
Riven: you might have some problems early, but after the first gank you should be able to effectively zone/harrass carry and/or support
Panth: also a weak early in exchange for counterharrass and good cc, as well as nice burst damage
Nidalee: just one word: Spears, no srsly. wonderful escaper, gap-closer harrasser and a nice heal