In reply to Nick_Merriman:
Based on too much experience with similar designs of bivvy bag, the options are-
1. Find somewhere sheltered to put you head
2. Pitch a tarp using a handy tree/bivvy pole or other suitable object and create your own shelter for you head
3. Do the drawstring up as much as you can. Position the hole near your mouth, roll onto your side and adopt the foetal position. Lie there hoping the rain stops soon. Any sleep will be disturbed by either rain pouring in the hole or the bivvy bag moving so you lose your air hole - both result in a damp and uncomfortable night.
Good luck!
p.s. option 2 is the best but obviously this is lots more gear than just a bivvy bag. Providing it's midge free this can be a really nice way to spend a night, especially if you're wild camping somewhere scenic