When we lived in a large 3-bedroom apartment we paid in the region of 200 aed (£35/ US$50) a month for electricity and water – and we had 3 air conditioning units on during the afternoon and evening: from 3pm to 11pm 5 days a week, and most of the day at the weekend. During the summer months, one unit feeding our bedrooms was on part or all night long.
Our current 4-bedrom villa, with 3 living rooms and a very large landing, is a much bigger space, and costs about 750aed a month during the hottest months and only 200 aed during the winter months. (We have 3 air conditioning units running through the night from April to October.)
We pay (and I think you will too!) by visiting the Al Ain Distribution Company office on Khalifa Street in the centre of Al Ain, and giving them the meter numbers. Some friends we have made here didn’t go to pay their bill until a year after they arrived! They didn’t get cut off!