Taking a conceptual look at the characters in main comic continuity:
Spider-Man is easily a bullet-dodger. His Spidey Sense makes up for his lack of bullet-protecting armor. Spider-Man doesn't just stand there to take bullets to the chest, he almost always dodges them.
Captain America is a slightly slower bullet-dodger able to definitively perceive at bullet-speeds.
Black Panther ... I can't say. His use of vibranium armor renders bullets inert when they strike his uniform, meaning that he doesn't typically have to worry about being shot. He is mystically enhanced through an organic herb that I beleive does enhance his physiology to supersoldier levels.
The Winter Soldier (Bucky Barnes) is not a bullet-dodger.
Batman (Bruce Wayne) is able to dodge Green Arrow's arrows but specifically designs his armor to withstand being shot. I would argue that Batman at his peak stamina can dodge bullets but the majority of the time he is an aim-dodger.
Nightwing (Dick Grayson) is way more agile than Batman, which I would argue places him at a bullet-dodger speed. His uniforms are not exactly bulletproof due to his need for flexibility.
Orphan (Cassandra Cain) is classified as a metahuman due to her superhuman swiftness. Orphan can easily dodge bullets.
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