They made sure to show that Quicksilver is only as fast, or almost as fast as a bullet, and that there are also limits to his powers, as we've seen him catch his breath a few times. So when he was saving Hawkeye and the kid, he didn't really have a lot of options. He couldn't run around the bullets, safely pick them up and move them to safety. Time doesn't stop for him. So when he was reaching Hawkeye, the bullets already almost hit them. And let's say he could have avoided the first bullet, there was no chance to avoid the countless other bullets fired by the Quinjet's mini-gun.
So even had he pushed them, he might still have been hit. But pushing might not even have been an option. We've seen that he can tear through robots with his speed. So at the speed he was traveling, a push might have actually killed them. Just watch the Quicksilver scene in Days of Future Past. He taps one security guard on the cheek with his finger. When time resumes that security guard gets knocked out cold.