So I'm replacing a ceiling fixture and my new fixture has a ground wire but the old one didn't. My outlet box has two places where wires come in - one with a black, white, and bare and the other with a black, red, white and bare. The bare wires are both attached to screws to the outlet box - I'm suspecting that these are my ground wires, but if they are I have no idea how to attach the ground wire for my fixture, both because the existing wires are so short and there are two ground wires in the outlet box but only one on the fixture. I've added a (not great) photo of my outlet box in case that helps. The fixture's mounting bracket does have a green ground screw on it as well.
The two bare wires are your ground wires, but they are not installed properly according to current codes (even though as long as the screws remain tight it should provide sufficient fault protection).
To be installed properly, there should be a "pigtail" from under one of the screws in the back of the box connected with a wire nut to the two ground wires AND the ground wire from your light fixture. That's a total of four wires in a wire nut.
The one on the left is horribly short. The one on the right is even shorter. Since you may be unable to connect them properly, you can try leaving the one on the right as is. There may be enough slack on the one on the right that you can pigtail it as described above (three wires in a wire nut).
Never wrap more than one wire under a screw. It's nearly impossible to get a solidly reliable connection with more than one wire under a screw, unless it's the type that has a clamping plate and is designed for more than one wire, but in that case you're not wrapping the wire around the screw.
If you find it impossible to use a wire nut because the wires are so short, go to Home Depot or Lowes and get some push-in connectors. They're similar to wire nuts, except you push the wires into holes (one wire per hole) like into the back of an outlet. (I don't like the "backstab" connections on outlets, and I'm suspicious of these connectors, but in this situation it may be the best option.)
The bare wires are the grounds, yes. In order to ground your fixture, you could remove the ground from under the screw in the top-left of the box. Wire nut it together with the ground wire from the fixture and a short (3") piece of bare copper wire (a "pigtail"). Screw the end of that short piece of bare wire under the screw. Make sure to use the appropriate sized wire nut (think you would want a red one here, which would work with #14 or #12 wires)