I finished tiling my bathtub surround over the weekend, and Sunday night I did the grout. I used 1/8" spacers (on 4 1/4" sq ceramic tiles), and non-sanded standard white grout.

I mixed the grout according to the instructions, coated the walls/wiped off the excess with the float, and waited about 20 minutes before wiping down with a sponge. It looks good from 4'+ away, but up close it looks like crap, as you can see from the attached image. The lines are bumpy and inconsistent. I've since tried scrubbing to no avail.

Is there anything I can do to salvage this?

Thanks!

You waited way too long to wipe with a sponge. Bet it was tough to get it cleaned off.
As you found out, the non-sanded grout dries very quickly. You didn't need to wait that long.

A couple options to try to make it look better.
You can get a grout saw and scrape out all the joints until the joints are uniform then regrout. This time wait only a few minutes after floating off the grout to wipe the walls. Use a damp sponge and a light touch.

Or you can regrout the walls to try to fill in the imperfections and see if you can make them look better that way. Again don't wait too long to wipe off the walls.

Or you can just leave it the way it is. Just because it may look bad up close doesn't mean the joints are bad in their effectiveness.

I was afraid that was going to be the answer. Would it be a huge PITA to remove it all at this point, using a grout saw?

You can try using the grout saw to smooth out the grout. Don't "saw" to deep.
If it works and the joints look better, seal it up w/ grout sealer.

Would fine grain sand paper work?

You have to make sure you don't damage/scratch the tile surface along the joints.

I have found that an old time beer opener, the one that punctures the top of the can in a V shape, does well in cleaning out the grout lines. Clean them out to a depth that is consistent and then re-grout. As the grout is drying use a smooth rag and wipe a few grout lines till it is the right dryness to leave a smooth surface and finish the job. As thin as the grout is going to be you may have to do this in sections because the grout is going to dry rather fast.