It is normal for schools to put two prospective grad students in one room during a visit. They usually only pay for you to visit too. One school I will be visiting soon will actually put me with a current graduate student.
You can probably upgrade to your own room but you will probably have to pay the difference yourself. The school might have a special rate with the hotel so this might not be as costly as you may think. I think schools would be understanding if you are visiting along with someone who would be part of your decision process (e.g. a significant other). When I visited (I was the only student visiting on those dates), the schools also paid for extra hotel stays outside of the visit days so that my wife and I could visit the city and my wife was also invited along when the profs took us out to dinner. But maybe I was just lucky with the particular schools I applied to. I was also visiting three schools in one trip so the travel cost to each school was pretty low.
I think you should write back to the school and explain that you would like to visit with another person and would prefer to have your own room. Negru is clearly trolling -- don't make it a demand, just state your requests and see what they say / ask how much they are able to compensate. Then decide whether or not it's worth it for you to visit them.
One school actually first told me that they can't compensate if I visit outside of Open House dates, but we decided to visit anyways. At the last minute, I asked the school if I could get their preferred rate at a hotel, and they decided that they would reimburse me fully after all.