Some cars have parking lights. Is the rear tail light on as well on the same side? I know that on my old cavalier when you turned the ignition off and turned the indicator stalk 'on', the dip beam would come on on whichever side I had indicated. Maybe the car has this type of set up and you have turned something on without knowing it. My old Merc had the same option.
I went for almost a year before I did this mistakenly once, until then, I didn't even know it had the facility.
If its not this and the switch is off, you would have to look at the switch, but then if you have taken the fuses out and the bulbs still work, it must be shorting or using a different circuit intentionally. can't think why only one would come on though, unless the bulb in the other one has blown. Try the parking lights thing first tho (it may be different stalk/switch that triggers these in a BMW).
1990 G 535i Sport Manual, Gas Guzzler but it puts a smile on yer face ;-)