The closest we see Pietro coming to move objects at super speed is when he is punching someone or moving them out of the way of the train. But all of these people are moving at normal human speeds, not the high speeds of a bullet.
He does come close, when he disarms (ha ha, get it?) Klaue in the salvage yard, on the Churchill. Klaue fires a single shot from his Beretta 90-Two Type F - 9x19mm (As identified at the IMFDb), but Pietro runs in, and takes the gun completely apart.
Only 9 cartridges. This gun is using the standard single-stack 10 cartridge magazine. The higher capacity cartridges are double stacks and look different. 9 cartridges on the table, plus one fired. As Pietro is clearly trying to show off, IF he could have grabbed the bullet that was fired, or the spent cartridge, in mid air, to put with the rest, he would have.
There's also the less convincing scene of Pietro trying to grab MewMew mid air and failing.
He attempts it, so he clearly thinks he can affect it. A regular weapon he could maybe move. Mjolnir is not being thrown at super-sonic speeds, unlike the typical handgun bullet, let alone a fighter jet cannon. It's sufficiently slow compared to a bullet.
But He is also shown having some repercussions from hitting things or running. Out of breathe, hand/shoulder hurts. Unlike his counterpart, he isn't immune to the laws of physics. Equal and opposite reactions. Inertia.
But as can be seen in the video above, the Marvel/Avengers Quicksilver is SLOW compared the Fox/X-Men Quicksilver.
He can be clearly seen while movie. Certainly high speed compared to normal humans, but in the scene where Hawkeye shoots the ground out from underneath him, the handgun bullet is much faster. In the scene where he gets grazed by a cop at the end battle, he's clearly not fast. X-Men Quicksilver is so fast that he takes out multiple guards and moves multiple bullets before Wolverine could even finish popping out his claws.
Water/rain and objects thrown into the air are almost frozen in mid-air.
And that's him goofing off really. Well, not even. In the sequel, a ten year older Pietro is EVEN FASTER, while STILL GOOFING OFF.
Plastic Bullets and Sprinkler systems are snails compared to a high energy explosion.
In short, MCU Pietro can't move fast enough to affect bullets at muzzle or near-muzzle velocity. And probably would be affected by Inertia if he tried.