You can replace Luden's with Everfrost depending on matchup, and you can also replace Void Staff with something like Deathcap or a tank item if you really need it or Zhonyas. Item order can vary, but I feel like this is the best item order. You could experiment with going like Horizon Focus after mythic or something though (explanation below).
Runes can vary, but of course Ult Hunter and Cheap Shot are must-haves. You could take ghost poro or zombie ward for extra vision if you're a support hardo, and you can take electrocute instead of dh for better laning. Transcendence gives some ability haste, since you only have 1 haste item with Cosmic Drive, and manaflow band gives some early mana.

Right. So you want to play AP Blitzcrank. From what I've seen, usually AP Blitzcranks have built maybe a lich bane and cosmic drive, but never Seraph's and Horizon Focus. That is such a huge mistake, you have no idea. First off, blitzcrank synergizes well with Luden's and Everfrost, and both of these items give mana, which synergizes with Seraph's. Also, since you have Seraph's, you won't really need Deathcap, since Seraph's alone has about the same AP as Deathcap, just without the passive. Now, you might have noticed I didn't include boots in this build. This is because Blitz has W, as well as Cosmic Drive's +20 move speed. This is also why you should max Q then W, since e doesn't really do anything except knock up and deal a little bit of extra dmg. Thus, on average, you'll probably be going faster than the average champ with boots. This is also why mana is important - you'll be spamming your W. The Mythic items are pretty self-explanatory, and so is Lich Bane (combo is Q E R so the enhanced auto from Lich Bane will do a lot of burst). Now, Horizon Focus is so important to AP Blitzcrank I probably would have built it after Mythic if not for the need of movespeed from Comic Drive and the burst from Lich Bane. This item gives bonus damage to immobilized targets, which is basically targets hit by Blitz's Q and E, AND it gives 115 AP. And, of course, for the final item you could build basically anything you want. I recommend void staff so you can deal damage to tanks too, but you can build basically whatever. At this point you deal so much damage you basically one shot any non tank or bruisers with Q + E. Oh, and did I mention that your R is on like a 20 sec CD with Ult Hunter? Yeah, it's pretty busted.

Since you're Blitz, you gotta hit your Qs. With a good synergy in bot lane such as Ashe or Twitch or something, you should be able to get early kills early, which gives you a lead. Afterwards, you should roam and try to look for some kills in the other lanes. Once you get ahead as long as you land your Qs you will be unstoppable. And btw start tear and two pots, then get support item first back, most preferably frostfang for the AP. You will sell this once laning phase is over to complete an item, or if you don't have an item to complete hold it until you have to sell it, since after that you will start farming (minions and kills). Try to get as minions as you can in laning phase though, as this build is quite expensive. If possible, have a friend play your ADC, except you get all the minions (kinda like fasting Senna), since no non-premades will let you just take their farm. You could also play ADC Blitz, but that has a really weak laning phase unless your support is something like Swain or Senna or Brand that does a lot of damage.