I've listed 3 different 'styles' you can go for in terms of builds.
The first being go full AP. You're going to do this in a couple of situations:
1) You get ahead/fed early.
2) You have a bad team and you feel it's down to you to carry.

The Semi-AP is what I go most of the time. I go a supportive build but add in Zhonya's Hourglass] and perhaps one other AP item. Even if you do decide to go fully supportive, consider getting at least a [[Stopwatch, you're a squishy champion who needs to go into a bunch of enemy champions to ult.
Your ult combos well with Zeke's Convergence too, and your ADC will benefit from the extra damage, not to mention it makes you tankier.
I see a lot of players buying Shurelya's Revelrie too, mainly for movement speed while ulting, however I prefer to take Nibus cloak which I feel gives enough movement speed.

The third option is to go a fully supportive item path, building like a traditional healing support. Your only shield is your Black Shield so in my opinion this isn't the best build for her efficiency wise. However, if your ADC is your win condition, and they're playing really well, just shield them, and peel them as well as you can, that's all you need to do.

• I only go Arcane Comet if I'm looking to go a damage orientated or build. The other half of the time I do go Summon Aery
• Look to roam when playing Morgana. Pick a pair of Mobility Boots and coordinate with your jungler to gank. You have good setup with your Dark Binding and your Sould Shackles.
• Think before casting your Dark Binding. Sometimes the threat of you throwing the binding is more crippling than the binding itself. Hold it until you're certain you can hit it, this means holding until after they use any dashes/ Flash if possible. This is something you can apply to Thresh and Blitzcrank hooks too.