Do you add an apostrophe or apostrophe s to princess?

The possessive form of Words that already end in s is subject to some differences of opinion, but personally I recommend that you just add an apostrophe, rather than an apostrophe and another s. Trying to pronounce two s sounds in sequence doesn't work very well, and you wind up sounding as if you are trying to imitate a snake. However, the plural form of princess is still princesses. With that added e, it can be pronounced.