There is nothing common on a Bronco that can task a 100 amp alternator. Certainly not a fuel pump or heater motor. You'd have to turn everything on and add a kicking amp for your stereo to drag it down if everything was working as expected.
A fuel pump is just maybe 2-5 amps. The whole engine running with EFI and pump and such is probably drawing less than 15 amps total. Just guessing of course, and have not bothered to add everything up for an accurate tally, but that generalization should get you in the ballpark.
An electric cooling fan can be a huge draw (or not) and a winch being operated can easily tap out a good alternator. But normal use? Nope. So something is definitely wrong with something.
I'm not sure how to test a 1-wire, but there might actually be a test port where you insert a metal rod/screwdriver/widget thingy to "full-field" it for testing. But to be accurate you'd still need an inductive ammeter to measure the total current.
You could turn everything on, then full-field it and measure the voltage at the battery. Should be nearer to 18v than 14 at that point I think.
But best to read the book before jumping into something based on hearsay!
Anyway your alternator's wiring could not be more simple. If it's a GM based 1-wire setup you only need to connect a large gauge wire from the alternator's output post to the battery positive. For conveniences this is usually at the starter relay where the batter cable attaches.
If you do indeed have a Ford 3G with a "1-wire" self-exciting regulator, you still need to connect the big cable to the battery, but need also to connect the Yellow wire to the same terminal on the alternator as the battery cable, if it was not done for you already.
That's actually how we get away with calling ours a "1-wire" because the Yellow wire is already done for you before we ship it, and all you need to do is connect one wire to the vehicle.
But either way you need only to connect a sufficiently sized cable to the battery and run with it.
The original Black wire to the starter relay stays in place, but the original Black wire from the back of the alternator does get removed and capped off like it sounds like you've already done.
An important thing you need to consider though is whether or not your alternator is bolted to clean metal on the engine with clean bolts and clean threads. If it's not, you'll need to add an additional wire to act as a ground connection.
I don't think they need to be the same size as the charge cable, but I've always done that anyway. If not exactly the same, I've still used at least a 6ga cable from the case of the alternator to the engine or frame or body.
If yours is already well grounded, and you know for a fact(!) that your charge cable is good, clean and tight, then we're back to the fact that you have a bum alternator. Period.
As said, it can be new and still bad. But I can't think of anything on the vehicle side of things that can cause a low-charge condition other than those things already mentioned.
Good luck.
Paul