Check out her body language! Typically, if you feel comfortable, she'll also feel comfortable—it's like a mirror. If you're feeling uncomfortable and awkward, you might be picking up uncomfortable vibes from her as well.
If she isn't asking questions, don't bring up the topic (if you don't want to). But it's likely that she's going to ask questions. Once you've gotten over the awkwardness...
Tell your family to keep your identity private so that nobody tells your dad. Make it clear that you don't want your father to know that you are bisexual by...