The first thing you should do is to remove any wax finish from the area that got splattered. Just the fact that the dye went right into the wood is a clue to me that there isn't much finish on this floor. First take some of that paint thinner solvent you bought and use either fine steel wool, or those FLAT nylon dish scrubbing pads (the white ones are non abrasive), and vigorously scrub the area involved. While the solvent is still wet remove it with a clean paper towel or rag. Let it dry for a while or speed it up a bit with a hair drier set on low. This would have only removed the wax and dirt from the finish. Apply a drop of water to that area, and see if it soaks in or turns the spot darker. If it does, it means you have virtually no finish on your floor (or as I say, an "unsound finish"). But if it beads up and stays there for several minutes, it means you have a sound finish, and the dye has colored only the finish.
Oh, and I might add at this point if the finish is unsound you could try a stronger solvent like Lacquer Thinner to remove the spots. And even the Xylenol in the product called Goof-Off Regular might work at this point, they are both cheap and worth a try.
So, if the floor finish is unsound, you should be able to remove the dark dye stains from the wood with a chlorine type bleach, but not the kind you were using. Better to use swimming pool bleach, called Shock Treatment (dry calcium or sodium hypochlorite). Mix the crystals with hot water, until solution is saturated. Apply to the spot and it should work right away, but try twice if needed and wait overnight. Neutralize the bleached area with vinegar, so it doesn t ooze chlorine droplets after the wood is finished. Wash it all off with lots of distilled water and let the wood again dry overnight, before refinishing, if it did work. Sometimes even this bleach will take too much color out of the wood, and you will need to replace some of the wood s tone with a light wood stain, before you replace the finish.
And as far as applying this bleach, you can either swab in on a large area encompassing all the dots in that region. Or (more difficult) apply it only with a small brush to the individual dots. Seeing how you will have to touch up with a wood stain anyway, the shotgun approach I think is better. The wood will have turned rough overnight, so gently sand it with fine steel wool, and add a splash a paint thinner to see what the final color of the wood when finished is. Like I said above use a light colored wood stain (Minwax has small containers and a variety of colors) to blend in the slightly whitened wood. Use a small brush for this, and if you have gone too dark, you can remove most of the wood stain with steel wool and paint thinner, let it dry and start again.
If all this sounds daunting, believe me IT IS, and even pros can goof up on jobs like this, so go easy on yourself (and your boyfriend if he's helping, and covering all costs, and taking you out for a really really nice dinner and show). Once you have the stain re-matching a bit, let it dry 24 hours or more. Now either apply a thin coat of paste wax on the area, or some orange shellac (check for too much of a color change with shellac) and then some paste wax. The shellac (if coated on the de-waxed area) will dry in almost any conditions, and once steel wooled will provide a better surface for the past wax to shine. Don't expect this to look perfect, but better than before.
If you were lucky enough to have found a sound finish, when doing that water test (remember the water drop test ?) you should be able to remove most of the stain by sanding lightly down through the layers of floor finish. Use 120 grit garnet sandpaper, and sand until the dots fade and disappear. Then determine what your floor finish is and re-touch the area, and consider re-coating the row of boards involved. You might ask, how do I determine what my floor finish is ? Well there is a section on this subject in my free floor cleaning article, the second part (worth a read might help you save your old finish). But to save you time I will paste it in right here. Do all these tests on the de-waxed area.
You can use various solvents to determine just what generic type of finish it is. The first solvent to try on the finish is alcohol. Use rubbing alcohol that you find at the drug store. Apply a few drops of this in a inconspicuous spot and observe. If, in a few minutes, it starts softening the finish and makes it sticky, the finish is shellac. This is the least durable of all the film type finishes so that may be why you are having problems washing the floor. A lot of people start waxing these shellac finishes and in order for this test to work you will have had to remove the wax with mineral spirits or paint thinner first.
The next step is to apply a few drops of lacquer thinner on a different area and watch this. If the finish is a lacquer or a water based finish, the lacquer thinner will start to soften it. Unless the floor has a pale look to it and has been resanded in the last 15 years, it's unlikely that it is a water based finish. To prove if it is a water based finish apply a few drops of toluene or xylene and if the finish softens it's a water based coating, and not a lacquer finish. If you find that none of these solvents affect the finish, you then have some sort of reactive finish, polyurethane varnish being the most common used on wood floors for the past 30 years. There are other reactive finishes but for the sake of maintenance and recoating it really doesn't matter.
So, if you had a sound finish, and now you know what it is, go buy some and apply a small amount to that area to see if it blends in. If the new floor finish is too light, again go back to the bare wood (paint thinner while finish is wet) and use a wood stain first, and then the floor finish, and Bob's your Uncle, you've done it !