The worst anxiety is before you tell someone. Often the reaction is pretty anticlimactic. Make sure your counsellor will keep it confidential and then just go for it. Even if she's not well-versed in gender issues, she can help you over some of the other difficulties that go along with it.
And I agree. I hate how people feel free to be homophobic and transphobic in front of others. I get it happening a lot now that I pass as a straight guy. You're right though, if she knew about you, she wouldn't say it in front of you. Now, if you don't feel comfortable saying anything, you'll have to bear with it, unfortunately. But the comments you're thinking seem pretty mild to me, like "it's up to them". It might send a message that at least she shouldn't talk like that around you.
And as for your coming out, you can never predict how people will react when someone close to them comes out as trans. Even when people have said stuff like that in the past, when it's a situation of someone close to them, they can turn into the most supportive allies. And the converse can happen. People you think are incredibly open minded can be bigots when it comes to their friend or relative transitioning.
Dennis