If the problem you're having is that it is too watery (I assume that's what you mean by "too thin"), there might be two causes:
The recipe you linked to calls for a sizable amount of stock/broth, relative to the wine. It might be assuming that you have something closer to homemade stock, which has a high concentration of gelatin, as opposed to store-brought "broth", which is more like meat-flavoured juice.
You might not have reduced it enough. A "thin layer" could mean anything, but it's not thickness you're concerned about, it's viscosity. When the sauce has been reduced enough, it should have the consistency of... sauce. As in thick, sticky, and slow-moving. If it still looks and pours like water, it's not reduced enough.
On the subject of taste, there's also the question of which wine you use. The wine sauce is going to taste like the wine (stronger, actually), which is one of the reasons why chefs will tell you not to cook with any wine that you wouldn't drink.
It's pretty easy to make a reduction - just continue to let water boil off until it turns into the consistency you want. If you overdo it, you can always add a little extra wine to compensate.
As noted in the comment clarification - if you're simmering at a reasonable temperature, expect to wait at least an hour, and for no less than half the water to evaporate.
If you're boiling something rapidly, and it's not in a terribly deep, narrow pot, then essentially all of the heat output of the burner is going into turning water into steam. The latent heat of vaporization of water is 2260 kJ/kg, so if you want to reduce something by a volume V, and your stove has power P, the time required is:
t = V * (1 g/mL) * (2260 J/g) / P
If V happens to be in mL, and P is in W (J/s):
t (s) = V / P * 2260
This would be modified slightly if you're using a really tall, skinny pot, since the convection within the pot, from the bottom to the top of the liquid, would be less efficient, with more heat transferred to the sides of the pot and out into the air, but I doubt you're actually going to try to reduce something like that. The P here is the effective power; for example, a gas burner wastes a lot of heat out the sides, so the advertised power will be higher. See TFD's answer for approximate efficiencies.
If you don't know the power of your stove, in all honesty, the easiest way to measure it would probably be to just see how long it takes to boil away a given volume of water, and work backwards. To get an accurate result, you should not boil a pot dry - once the water is a thin enough layer, the heat transfer might start working differently, with the pot itself heating up more, and water splattering. So you could, for example, put in a liter of water, boil away at the stove setting you intend to measure until it's substantially reduced in volume, record the time, then pour it out to measure how much you boiled away. At this point, knowing the power output might be overkill, though; you can really just measure the time per volume reduction, and use that, unless you care about the power for other reasons.
Trying to deduce the power of the stove from, say, the temperature of an empty pot or of the burner without a pot on it (assuming it's electric) would be difficult; you'd have to deal with the heat transfer between metal and air, and the convection in the air.
Dependence on ingredients shouldn't be significant - you're still just boiling water, unless there's a substantial amount of alcohol, in which case the latent heat of vaporization will be different. Pure alcohol has a latent heat of vaporization of 841 kJ/kg; I haven't found a good table for mixtures.
For solutions, as I noted in the comments, the latent heat of vaporization should be that of water, plus/minus the heat of solution of the solutes (I forget which direction that's measured in). The most common solutes are probably salt and sugar, which have heats of solution of 70 and 16 J/g, respectively. (I found this table, and converted.) The next most common thing I could think of that might be present in substantial concentrations is citric acid; this paper reports a heat of solution of -57 J/g. In all these cases it's small compared to the latent heat of vaporization of water, so pretending the liquid is water should be a good approximation. It's possible that things change if you're reducing really far: heat of solution does depend on concentration. That is, things are different thermodynamically (statistical mechanically?) in a nearly-saturated sugar syrup than in slightly sweet water.
Best Answer
It sounds like you cooked it too long, and additionally, the recipe may just be bad. If you managed to cook away all the liquid and end up with just wine-infused bacon, there was probably a point before then with a reasonable amount of liquid. Sometimes what people are going for with wine reduction sauces is really to have a lot of the wine flavor concentrated into some minced ingredients, with enough thickened liquid to hold it together a bit. If you crumble the bacon finely enough, and don't reduce away all the liquid, you might find you like it like that.
But it sounds like you're looking for more of a liquid sauce, and at the point when enough liquid remained, it was too thin. I'd might suggest just finding a more detailed, trustworthy recipe for a wine reduction sauce, and just adding in bacon (and maybe taking out some other ingredients).
Short of that, if I were going to try to do this without many extra ingredients, I'd:
This is again a very fuzzy recipe. With the amount of fat bacon releases, you can definitly make more than enough roux to thicken plenty of sauce - depending on how much you reduce the wine and how thick you want the sauce, I'm guessing you'd only need a tablespoon or two of roux. If you feel you've lost too much of the bacon flavor, see SAJ14SAJ's answer for how to incorporate more of the fat without the sauce separating.
(In general, you have to be careful with vague recipes like the one you found - they'll tend to assume you know some things, so if you can't fill in the gaps yourself, it may be best to find a more specific one! And sometimes they're just bad recipes. That one tells you to fry bacon in olive oil, which is really suspicious - you don't need extra oil to fry bacon.)