Mikvaot usually provide private facilities in which women prepare themselves. Bathrobes and towels are usually available as well. You can ask ahead about this and bring your own if it will make you feel more comfortable. You can wear a towel or robe until you reach the steps of the mikveh.
The mikveh attendant is not required to help you inspect your body, so you can request that she not do so if it will make you more comfortable. Even if an attendant does look at you, she is looking for stray hairs and the like and is not at all focused on your body itself. The water provides modest cover when you are in it and most mikveh attendants politely look away when you go down into the water and when you come out. You can ask the attendant to do so, explaining that you are shy. The attendant is only required to see that all of your hair goes under the water. Beyond that, you can feel confident that she is not looking at you.
We think this should be manageable. If it should become a problem, please write back to us for further suggestions as to how to handle the situation.