Brand "support"

Then the ADC bot lane should act as if he were laning against a mid laner who's roamed bot. I have played Ashe against fed Katarinas, Akalis, even LeBlancs, and respected the fact they got burst and made it out of lane with farm alive, without even using my ult.

Heck, I've even played against a Heimer - Blitzcrank bot lane and ended up 0/4/0 by the first few minutes, but still respected that Heimer was a mid laner and not an ADC. I eventually got ganks from Renekton, who was more capable of getting kills on such a high damage zoning duo than the engage-heavy Leona (who started roaming mid instead) and set them behind.

There are two ways to beat the Burst Support:

1. Ganks, even if the support is dead and you're left at 2v2 (jungler + ADC vs Mid laner + ADC/supp), Diana jungle will trump Morgana if the enemy support has burst, due to the fact non burst supports have strength in countering tanks and sustained damage, not in countering assassins and mages (which is why junglers love ganking mid). For example: The jungler is Zac and your support is Lulu, Lulu dies from a single spell rotation but Zac comes in to engage anyway. Zac has an advantage against burst due to being tanky, while the enemy ADC has to focus on Zac before he kills the support, the ally ADC who is in a safe position gets to choose which of the two is more important.
2. Play passive, burst supports rely on having as much resources as a mid laner, but due to having no gold and reduced EXP, they have to get kills. By staying alive, the lane is being pressured by the fact roaming will have the risk of a dead ADC or tower.

I've applied these two strategies against Vel'Koz, Zyra, Annie and Anivia. They have their power and personally I like playing Anivia or Vel'Koz as a support, but they have plenty of counterplay too

Being treated as a support while having mid lane burst is a dream to most.