Learn German: Ist ihr Bad groß? - Is her bathroom big?

The ending of a possessive word depends on the gender of the noun that follows it. Bad is a neuter noun (das Bad). In the nominative case (the subject of the sentence), neuter nouns take the basic form ihr with no extra ending. If it were a feminine noun or plural, you would use ihre.

Couldn't ihr also mean "their" or "your"?

Yes, absolutely! Out of context, ihr can mean "her" or "their". Also, because the first letter is capitalized to start the sentence, it could be the formal "Your" (Ihr). You would need the surrounding conversation to know exactly which meaning is intended here.

Why doesn't the word groß have an ending like großes?

In German, adjectives only get extra endings when they come directly before the noun they describe (like in ein großes Bad). When the adjective comes after the verb (like here with Ist), it stays in its basic dictionary form.

Is Bad the same thing as a bathtub?

Bad is the common short word for Badezimmer (bathroom). A bathtub is specifically a Badewanne. In everyday German, it is very common to just say Bad when referring to the room.