Have been a Ziggs main mid for a while, and not tried bot lane but can understand the issue.
Q has long reach with bounces but should be easy to dodge as well
W has that nice hexplode on towers a 25/27.5/30/33.5/35% HP which gives people the scare that they can't hold a tower near death but this is mute fact as any good dmg adc can take that turret's HP down fast too, he just has a safe distance from it. It is his 1 OP skill and only works on Towers and not on Inhibs so I don't think it's worth nerfing without giving him a major buff elsewhere or else he's likely to not be picked hardly ever then.
E is a nice slow but only if you get them to hit and too many champs have rolls, dashes, and charges that cancel them out, the ones QQing over it are the ones who don't have that.
R is a nice ult, but has already had it's range reduced once before and it's not any more powerful than Lux's or EZ's long single line ult and yet it still got nerfed a few patches ago with how it only does max dmg if they are in the center so just moving 2 steps nullifies over half the dmg. If anything I'd call for a slightly large AOE and a 3 ring circle, Center being max dmg, middle for 2/3rd, and outer for 1/2 dmg. Since so many have dashes, like Yasuo, Jax, Zed, and Fiora who can exit it entirely as well as Flash, then maybe it's a nice idea to make it more of a good hit. Or lower the CD on it to give him more chances to hit since many of the other champs are getting where the CDs at 40% CDR on their ults are only about 25-35 seconds.
I do like the idea of Armor/MR on towers and letting penetration work as you already DO have some of that on them already without the pen working. And as far as him in bot lane being overbearing, it's only cause bot lane ADC/Support combos are use to fighting other ADC/Support combos, changing out for a mage/Support combo is giving them issues cause of his Q range, other mages are at a shorter range anyway usually or should be the more annoying ones that AREN'T getting mentioned that can CC and attack an ADC outside their range, like Ryze, Cass, or Syndra. However with his lack of healing and his already squishiness they shouldn't have a problem with him, it's just they are dealing with more AOE abilities and not knowing that they need to dodge until his mana is gone and then dive on him. His minion clearing shouldn't be any more than a Jinx clearing with Rockets or a Tris clearing with her E's? passive that explodes minions she kills with AA. His CD and mana consumption on his Q make it where if he uses it constantly to minion clear and push, he's opening himself to be oom when he gets up to tower and they can dive on him easily.
I've said this is some other posts about Ziggs, I personally think he needs a bit of a buff in the self healing department as he's getting beat out by Ahri, Akali, and Ryze as well as others, in that area who have scaling healing/shields in their abilities in addition to what items can give them. Also many seem to have higher mana regen or lower spell costs as I've seen them throwing spells as often as I am on Ziggs and they are at nearly full when I'm below 50%. This forces me to build specific items to compensate for that that usually get me fussed at by my team for what i'm building, Hextech Gunblade especially as it's the best healing I can get, only other option is Rod Of Ages which only heals on spell USE for a max of 25 per spell. HGB will still give 5% of the aoe dmg, and 15% on the single target dmg. It works but requires a high gold cost when compared to how an ADC can grab a Vamp Scepter early and get the full 10% Life Steal to heal and focus on their dmg and crit items before building it into BoRK, BT, HGB, or Ravenous (if melee) to get the same or a bit more LS. With his lack of Hard CC and Self healing all he has is his ranged dmg and his W hexplode on towers to make him a champ people will pick, many are still preferring Ahri, Lux, or Syndra in mid most commonly.
).
+
, assassins with sustain supports
+
, mages with dissengage supports 
who can now push you to tower and slap the shit out of you for free
free farm
all have a long range and can be played similarly to ziggs and xerath
and 
so that Ziggs can use mana to poke enemies under tower.
(sustain) 
(easy combo) 
(peel) 
(???)
if you're feeling cheesy
