This might seem like a silly question/suggestion... but would she find it easier to write things down beforehand? Specific questions she has, issues she deals with... that way it 'might' ease some of the anxiety down when she comes face to face with the therapist as the potentially awkward part is (opening up) is all written down for them to read.

I don't have selective mutism, though when it comes to 'opening up' especially with strangers, I find it very hard... so by doing the above first in the comfort of my own surroundings (home), it does help.