She would be injured, but she does have superpowered healing abilities
During the first battle scene on Themyscira, Diana does sustain an injury/flesh wound on her left arm which the movie seems to imply was a deflected bullet.
This happens when Antiope sacrifices herself for Diana (probably deflecting the trajectory of the bullet to save her)
This implies that the DCEU version of Wonder Woman, at least at this point in her timeline, can have her skin broken by bullets or kinds of trajectories (like shrapnel).
Later on, though, the healer removes her bandages and sees her skin has healed fully, surprising her
Comic book guru
Depends, in some stories she’s bullet proof, like in Injustice
In some she’s not
Though that one above is a little more complicated than her just being shot by a bullet.
Then there’s always the strange times in comics like that time she got shot in the rear
To put it simply, it’s inconsistent. She’s durable but has usually shown vulnerability to piercing objects.
Been reading about superheroes for decades
For a long time, bullets and arrows could harm her by penetrating her skin because the force of the bullet (or arrow) was concentrated in a very small area. (I suspect it was also because if bullets didn’t hurt her she would have know reason do to her bullets and bracelet thing).
It may turn out that she has more vulnerability to bullets than she thinks and just hasn't been hit in a while. That would make sense… in this day and age, WW should be able to handle a bullet, especially considering everything else she can handle.
B.S. History & Philosophy, University of Autodidacts
I am not a long-time follower of the Wonder Woman character but it is my understanding of her bracelets that they not only deflect bullets but absorb some of the energy which she can tap into later.
Examples: on Thymiscira while sparring she absorbs many sword strikes and when she crosses the bracelets they emit a powerful shock wave.
In the final battle Ares brings down lightning which Diana absorbs into the bracelets and then redirects at Ares, killing him.
As far as being wounded, of course. If she could not be wounded like the other gods how could they be killed? But unlike those other gods Diana has the advantage of invincible plot armor.