Disclaimer: I'm not a teacher.
You can certainly say "less cheap" or "a bit less cheap". My intuition is that "a bit less cheap" suggests that something is still fundamentally cheap (even if it is not as cheap as the thing it is being compared to) whereas "a bit more expensive" emphasizes the fact that you'll have to pay a little more. It may be more common to use "less cheap" in the sense of "less shoddy" than in the sense of "higher in price"; in general, "more expensive" strikes me as less convoluted than "less cheap."
There's no rule preventing you from saying "less cheap", though. If it's uncommon, I guess you can chalk it up to usage.