It appears that the building is near Safa Park. You may want to look at furnished serviced apartments (studio) near Al Basha where there are plenty and you can take the train. Most of the apartments between Trade Centre Roundabout and near Safa Park are unfurnished and pricey. Another forum that may give you more info and help is
http://www.expatforum.com/expats/dubai-expat-forum-expats-living-dubai/ Another alternative is to look for someone who is looking for a roommate. (Check dubizzle.com and expatforum.com) Make sure it's a male roommate!!!! Just be careful as to location and most likely you would prefer a western roommate.
I forget to mention: be very, very careful who you deal with!!! There are many people who got scammed. Make sure you get receipts and give a check whenever possible. You should also know that bounced checks can cause a big problem so make sure you cover every check you write.