Topherallen,
All is not necessarily lost.
First, make sure you are watering properly—that is, often enough without overwatering. This can be very tricky as the top can look bone dry and the bottom still wet. It’s dependent on whether or not you have a good draining soil.
Second, make sure it is getting adequate light.This means usually being placed in a room with an east or south facing exposure. I'd suggest the brightest room in your house. But, I have read that you shouldn't put it in a window sill, because the direct sunlight can heat the pot up much more than you realize.
Regarding humidity, most homes have far less than people believe. It may be 50-60% outside, but in your appt, the air conditioner/heater has depleted humidity levels to less than 30%. Some sort of misting is usually suggested.
As for whether or not a boxwood can be grown indoors, I'll leave that up to more experienced growers.
I would suggest checking at
http://www.bonsai4me.com/. There are several good links there on bonsai basics, watering, and species guides.