You must bathe and wash your hair some time during the day on Friday. You need to use warm water at least for washing your hair and the creases and folds of your body. If no bath is available, you can wash yourself thoroughly in the shower. You can bathe any time after sunrise, and can do so anywhere (a friend's house, a local gym, etc.). You could put your hair in a ponytail or a bun to keep it from getting knotted. Other elements of preparation (e.g., brushing teeth) should not present a major logistical problem. You can shave and cut your nails a day or two in advance, as they do not grow back that fast.
Although Ashkenazic practice is to conceal the night of mikveh immersion, it is ok for a few people (preferably women) to find out about it if that is the only way you can properly prepare for mikveh.
At the mikveh, you could run your fingers through your hair to remove any loose hairs before you go in the mikveh (make sure you do not pull out any hairs!). You wet your body, inspect yourself, and immerse (see Immersion on Shabbat and Yom Tov).
Hairwashing and bathing in warm water are prohibited on Shabbat, so even at home you cannot wait until Shabbat to bathe. If you still do not see how you can prepare, please get back to us with specifics of the problem so we can try to help you further.