Count of getting over it as a natural recourse of living with - and doing everything with - your entire platoon in boot camp. Whatever shyness you're feeling now will go away very quickly as the system is designed to help you adjust to military life in a quick and efficient manner. You'll have much more to think about than being shy about anything so relax and enjoy yourself in your new lifestyle.
Taking a leak will be the last of your worries. Trust us... you'll drink so much water, your bladder and kidneys will feel as if they are about to explode! You'll reach that point in Boot Camp where you and other recruits will literally double up, even triple up at the urinals.