You can reach Bernice Lake by taking a small detour on the way between Vogelsang and Lake Merced High Sierra Camp.
Apparently it was named after the wife of a park employee, if Wikipedia's English version is to be believed.
The lake looks very isolated; it takes between a day and a half to two days to hike here from the usual starting points (Yosemite Valley or Toulumne Meadows).
So if you are looking for peace from the hustle and bustle and solitude, this is the place for you.