Having a mikvah attendant is not just an expectation or a stringency, it’s a halachic requirement. The primary role of the attendant is to observe the tevilah to ensure that all of the hair is submerged. If even one hair is floating on the surface of the water, the tevilah is not valid. This doesn’t mean that we don’t trust a woman to immerse properly, but that it’s impossible to see what is going on above your own head while you are immersing.
If you would like some private time in the mikveh, you can ask the attendant to leave you alone for a few minutes after you have completed the halachically required immersion in her presence. It would probably be easiest to discuss this with the attendant when she comes in to check you, before you go into the water. In a mikveh where many women take turns immersing in a single mikveh pool, you will need to figure out how to let the attendant know when you have come out, so that the next woman can go in.
Many mikveh attendants are trained to be extremely sensitive. As you have noticed, they do generally turn around until you are in the water. (If an attendant does not do that, you can certainly request it.) Once you are in the water it is very difficult to see anything under the waterline, so your body is basically covered.
If you are still uncomfortable, you can make arrangements with the mikveh attendant to have a friend or someone else you are more comfortable with oversee the immersion. This can be any halachically observant Jewish woman over age twelve.
Please see here for further discussion of this question.