General consensus confirms that Zer0 absolutely sucks at sniping in UVHM. I'm currently using a melee/gun hybrid with the legendary COM that does some decent damage, but I still die a lot. People like full melee for absolutely destroying people with Zer0.
Some doors are best left closed, because once open, they're easy to walk through again and again. -- GT: Wretched Owls
I sniped with Zero early on in UVHM (before getting my melee gear) and did quite well. I filled out the sniper tree, used a sniper class mod, and made sure to use a Jakobs sniper rifle (Jakobs rifles have the highest base damage overall and often have further boosts to weapon damage and critical damage). A Bee shield is also very good to have.
Don't forget to take advantage of Deception when sniping. Even without the Bee's amp, I was getting one-shot kills even on nomads and bruisers because I went into Deception and waited until the last second of it to fire, to maximize the damage bonus. A cooldown relic and a bit of patience can take you through even the toughest areas without a scratch. Usually, if you snipe someone in Deception (and you're far enough away), the enemies won't even be alerted.