As you have written the sentence, you should use the plural "bounds".
0 and 20 are the lower and upper bounds of the set S, respectively.
"0 and 20" is a plural subject, with a matching plural verb "are". 0 is one bound and 20 is another, so "bounds" is most appropriate.
You are free to include or to omit the definite article before "upper". I think omitting it (as in your example) is the better choice, but that is an assessment of style rather than grammar.
Alternatively, you can use the singular "bound" after both upper and lower:
0 and 20 are the lower bound and the upper bound of the set S, respectively.