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.
You could use any number of methods, including:
Starch Thickeners (added as a slurry)
One of the simplest and most straight forward: dissolve some starch (cornstarch is common in the US; alternates include potato starch, arrowroot, or tapioca) in some water, into a smooth slurry.
Add the slurry to your simmering sauce base, stirring, and let it cook for a minute or so. As long as your sauce is at the simmer, it will come to full thickness very quickly.
Add slowly until the desired thickness is reached.
Flour slurry
The technique is similar to using a pure starch: create a slurry of flour in water, enough water so that it will pour easily.
However, you will want the sauce base at a boil, as flour thickens at higher temperatures. It will also add more cloudiness to your sauce (probably not a factor with your recipe).
Add slowly until the desired thickness is reached.
With a beurre manee (butter kneaded with flour)
Knead equal parts of room temperature butter and flour together.
Add slowly to your boiling sauce, while whisking, until the desired thickness is reached.
With roux (flour cooked with butter)
Melt butter in a saucepan. Add an equal volume of flour, whisking it in to prevent lumps. Continue cooking for a couple minutes. You can use this right away, or save it in the refrigerator to use later.
Add roux to your boiling sauce base, whisking, until you achieve your desired thickness.
All of these starch based methods will thicken about one to two cups of sauce per tablespoon of starch, depending on how much additional thickness you desire. The exact ratio of thickener to sauce is up to your taste.
All of the starch based methods should be done at the end of the cooking period, prior to service.
Reduction
Simply reduce your sauce until it is as thick as you desire. This may overcook your mushrooms so may not be an ideal method for your recipe. You might also reduce your sauce to almost the desired thickness, then add the mushrooms. Your sauce is very, very high in fat (butter and marscapone, so it will not likely break).
More mushrooms (and a blender)
Add even more mushrooms to your recipe. When it is cooked, remove some mushrooms and reserve them. Puree the remaining mushrooms and sauce in a blender or with an immersion blender (or even with a food mill). Add the whole mushrooms back for flavor. The body of the pureed mushrooms will add thickness to your sauce.
This method will work even better if you add some potato chunks with your mushrooms. This gives the benefits of the potato starch, and more body from the potatoes when you puree.
Best Answer
To thicken anything
'like a bechamel sauce'you would use a roux.You could just add flour to the cream, or any other liquid, but it should be added to a small amount of the liquid and form it into paste. Then return the 'paste' to the rest of the liquid and heat until thickened (it will have to boil).A roux, however, is a richer base for a sauce. Start with equal amounts of a fat (butter, olive oil, sausage drippings...) and flour. Get the fat hot and then whisk in the flour until it has absorbed all of the fat into the flour. Then add your cream and heat, still whisking, until thickened.
If this is not what you are after, please be more specific. Perhaps describe what your end goal is. This can be used to create anything from sawmill gravy to nacho cheese sauce, depending on what you add to the cream or milk afterwards.