status

She's single. And Its seems that she don't have public dating history. And she denies having dated Zac Efron when they shoot The Lucky One. She's very private.

Aren't there other single Hollywood hunks that the media would love to pit her with considering her rather meteoric rise to fame?

She is dating a woman, the creator of Portlandia. Her name is Carrie Brownstein. They were friends awhile then started dating and went public in like April 2015 I think. You can easily google it, it was in a lot of magazines at the time. So, apparently her bisexuality isn't just for OITNB ;)
http://www.celebdirtylaundry.com/2015/orange-is-the-new-black-star-taylor-schilling-new-lesbian-girlfriend-carrie-brownstein-couple-spotted-together/