Salam!
You can follow verbs of perception (see, hear, watch, listen to) with either the base form or the -ing form of a verb. In many cases, there is no real difference in meaning. I think that this is one of those cases where you could use them pretty well interchangeably.
There is a subtle difference, however. The base form suggests a single completed action, which is why Jesse says that "It would be nice to hear her sing" might suggest one particular song: heard in its entirety. Meanwhile, the -ing form suggests the action or process of singing.
[NB The 'singing' of "I'd like to hear her singing" could also be interpreted as a verbal noun, as Kylie Alonso suggests. This is because of the ambiguity of the pronoun 'her'. But let's presume it's a verb here, as in "Would you like to hear me singing?" (verb) as opposed to "Would you like to hear my singing?" (noun).]
Here's an other example which might be a little clearer:
Compare, for example, "I heard you singing in the shower this morning" with "I heard Pavarotti sing at La Scala in 1983". The first sentence suggests that I walked past the bathroom door this morning and just happened to hear you while you were singing : this focuses on a few moments of an action that was in progress at a particular moment. By contrast, the second sentence refers to an entire concert which you heard from beginning to end.
I hope that helps.