What kind of "weed killer"? Different ones do different things and unless there are weeds there now, some won't do anything to bare ground. On the other hand, products that would be effective on bare ground for some time into the future, might also damage nearby plants, depending on what is in the vicinity, of which we have no knowledge.

Usually, it is so dark and unfriendly to all plants below decks that weed growth is not prolific. I've always taken care of it like any mulched bed ... shoot active weeds with glyphosate and apply preen on a schedule to keep future weed sprouting to a minimum. Once weeds are controlled for a couple of years like this, barely any more come to hang around. Weed "barrier"/fabric is ultimately not going to help. A good layer of mulch will help, though.

RM43 43% Glyphosate Plus Weed Preventer or maybe Roundup Grass & Weed Killer Super Concentrate...?

The entire space is currently bare dirt.

No point in spraying glyphosate on bare dirt. Only works on growing plant foliage.