Just fire away, possibly with drill before driver, for each screw,
locating where you guesstimate there's framing below. If you miss, try
again nearby. Any problem with a few "spare" holes in your new hardwood
subfloor? Didn't think so.

Of course, there are simple strategies to reduce misses, if it matters.
E.g. locating approximate joist center at each extreme of floor area,
than marking line between pair of points for rest of holes to joist.

I assume you mean "real" screws, not crappy brittle drywall screws.
Like, deck screws.

HTH,
J