The best way to get her to show her face. Is probably to comfort her about it. I mean, just let her know you don't really care what she looks like. Whether it's burnted, scarred, nothing but skin... I mean... how does she eat and drink?!

but as I was saying. Just let her know that even if it's the ugliest face known to man, you won't treat her any different. Unless it's treating her better.