Having a shared dream instead of approaching her is very impractical. The trouble is that most shared dreams happen between people who know each other quite well, and here you hope to have with someone because you *want* to get to know her.

Besides which - in a woman's mind - if you can't drum up the courage to talk to her, then you're probably not worth it.
Put aside your fears and worries and chat to her about something she seems to be interested in.
If you can't find anything, just look for any old thing. Favourite colour, mannerism, school subject, teacher, whatever.

If you really don't know what to say, just say you think she's cool and what hobbies does a person like her have. Then show an interest in what she likes and ask if you can tag along to something. Just cos it's cool.

I know it sounds difficult and 'left field'.. but once you're past that you'll wonder why it was so hard.

Now, if you really want to bring dreams into it - try have a lucid dream and recreate the situation of speaking to her.
If your fears come out (they might), then remind yourself that it's a dream and keep badgering her and confronting the fear.
It'll help you drum up the courage to approach her.