Although not in LA, there is one in Thousand Oaks called "Nothing Bundt Cakes:"
We tried the chocolate and the lemon...nothing special. I was hoping for something very moist, with perhaps a divine filling. But they do a terrific decorating job for special occasions, so it makes a nice "gift." You can view their creations on their website.
Nothing Bundt Cakes
1610 Thousand Oaks Blvd. in Thousand Oaks
They have several other locations.
Kiss My Bundt is supposed to be opening at 8104 W 3rd Ave:
They are predicting a late April/early May opening: