It sounds like the woman might be insecure herself, and overcompensating by being bossy. Since this is her project, and you know more about testing and field work, she might feel threatened by you.

A few ideas...

...List a few things you like about this woman. Spend some time really thinking about something good. It could even be that because of her project you have a job. Whenever you start to feel frustrated with her, call up the list of 'good qualities' in your mind and try to focus on them.

...Act like she has a PhD. Let her boss you around and do your best to be respectful. If she is insecure, the more you treat her with respect the nicer she might be to you.

HTH