It matches сумка. If you were talking about a permit (masc.), you would say Ей нужен пропуск. If you were talking about a taxi (neut.), you would say Ей нужно такси. If you were talking about anything plural regardless of gender, you would say Ей нужны столы, тарелки, яблоки, etc.
Can someone please explain a little further the differences between "надо, нужна and нужно"?
Надо still means need, but I read in a previous lesson that it's not used for nouns. нужна is used for feminine nouns, нужно for neutral and нужен for masculine. нужны for plural.
надо needs a verb.
Мне надо спать. (I need to sleep).
You can use нужно (only with о) in the same way.
Мне нужно спать.
When referring directly to a noun you can't use надо. You have to use нужен, нужна, нужно, нужны, depending on the gender of the noun that is needed.
Ей нужен стул. (masc.) She needs a chair.
Ей нужна бутылка. (fem.) She needs a bottle.
Ей нужно молоко. (neuter) She needs milk.
Ей нужны очки. (plural) She needs glasses.