Doing something sheepishly means expressing your embarrassment and shyness about it, like when you sheepishly admit how much you love watching soap operas on TV with your grandparents.
When you think about how timid and shy a flock of sheep can be, the adverb sheepishly will make perfect sense. Anyone who acts in a way that betrays their shame and bashfulness is behaving sheepishly. You may smile sheepishly at your dad when he discovers you ate the last brownie or shrug your shoulders sheepishly when you teacher asks why you didn't finish your homework.