Since when has Bass ever been a cornerstone of our team? Regardless, if Bass is traded it'll probably be alongside other parts and/or picks in order to upgrade at his position. Don't see us trading Bass for a 1, 2, or 3 with the logjam we have at those spots already. So to answer your question, yes, we'll be okay.
I doubt White is on our roster next year and this draft will have some bigs in the mid-teens that could contribute immediately (Olynyk, Plumblee, etc.). So we could conceivably draft Olynyk or Plumblee, have Sullinger back, use the MLE on a serviceable big man, and upgrade the Bass position in a supposed Bass + parts off-season trade.