Opposite of "bells and whistles"
Solution 1:
I would call those the nuts and bolts.
- Fig. the mundane workings of something; the basics of something. (See also get down to the nuts and bolts.)
I want you to learn how to write well. You have to know the nuts and bolts of writing. She's got a lot of good, general ideas, but when it comes to the nuts and bolts of getting something done, she's no good.
Solution 2:
I would say that things that are opposites of bells and whistles (that is, they are not optional) are essential (adj.) or essentials (noun). Another noun that would work is necessity.
Edit: Since a more metaphorical example was asked for, I shall provide one that I think fits decently: meat and potatoes. The meat and potatoes are the basic, necessary things; this is the opposite of bells and whistles.
Solution 3:
Having lived on both sides of the Atlantic, I can confirm that 'meat and potatoes' is used not only by North Americans, but also by English-speakers across the pond. I believe both 'meat and potatoes' and 'bare bones' work in this context.