wrote

I am doing a tile project - installing ceramic tile over an area that
was originally carpeted. It is in a bathroom, on a second floor.

Not mentioned by others but be sure it's not going to be too heavy. Some
tile types are quite heavy. I'd tend to the vinyl tiles in a 2nd floor.
You can find out for sure with a structural engineer but they are pretty
pricy.

When I pulled up the carpet right along the shower, there is black
mold on the wood subfloor. I'm pretty sure it's not a leak, just the
shower usage and dripping when the shower door opens. There is maybe
a square foot area with this issue.

Is the wood firm as the rest? Not soft in spots? Then you are probably
right and it can be covered after treating.

Is there anything I can or should do to clean it up? Can I bleach
it? Seems like putting any liquids or cleaners on wood is not a good
idea. Maybe put a layer of the Killz primer on it?

Bleach will be fine if the wood isnt rotted. Use a spray bottle with 50%
bleach and 50% water, wipe up well, and reapply. Actually pouring it may
not be a good idea if you dont have a tight water seal against the wood and
wall (or might be shower it seems). You dont want it dripping down through
that to whwatever it may hit underneath.

Cutting out the section and replacing is probably not feasible, at
least not for me to do, I'd have to go get a contractor for that I
guess. The whole shower would have to be removed I think.

As long as the wood is ok, just stained, you should be alright. Seriously
though, careful on the weight of the tiles. You didnt mention how big the
room is or the floor joisting, only a shower which to me seems to indicate
an added bathroom in an older house. If it wasnt built to handle the weight
of a full tub, it may not take well to ceramic tile either without
reinforcement. Vinyl tiles will not be a problem at all.

Looked at an old house once, Mom was thinking to refinish. We backed out
before signing once we checked that aspect out. They'd added a 3rd floor
bathroom and then tried to tile it and put in a tub. They overloaded the
weight bearing and you could see cracks that had developed in the ceiling
and walls below it. It was the upper limit of our finances to get that one
and a really big job, but we could have fixed it (had structural engineer
look, hadnt been edited for the bathroom long and the damage was mostly
cosmetic at that stage but would not remain so). The fix would have been to
remove the tile and tub and put in a smaller pedestal sink and a plastic
type shower enclosure (then replace some 19 sheets of drywall).