Learn Spanish (Latin America): ¿Te basta con un vaso de agua?

Bastar (to be enough) works just like gustar. Instead of saying "You have enough," Spanish logic says "It is enough for you." The pronoun te means "to you" or "for you," and basta provides the "it is enough" part.

Why is the word con used here? The English translation doesn't say "with".

In Spanish, the expression bastar con is commonly used to say that a specific thing is sufficient to fulfill a need. The literal structure of the Spanish sentence is "Is it enough for you with a glass of water?"

If I were offering two glasses of water, would basta change to the plural bastan?

Not in this exact sentence! Because you are using con, the verb is impersonal (meaning "is it enough with..."), so basta stays singular. However, if you remove con, the glasses become the subject of the sentence, and the verb must change to plural to match them: ¿Te bastan dos vasos de agua?

Why isn't there a Spanish word for "is" or "it" at the beginning of the question?

Those words are already baked into the verb basta (it is enough). Just like me gusta means "it is pleasing to me," Spanish verbs don't require a separate dummy word for "it" to act as the subject.