I wouldn't say, "What a bummer that you didn't hear from your bio mom" - maybe it's NOT a bummer for her, so don't presume you know how she will react. I would not suggest you call the bio mom - it's not your place, it could be perceived by your SD as stirring the pot that's better left on the back burner. While it may be that the bio mom is grateful to you for providing a stable home, it may also be that she is jealous, resentful and guilty. So you trying to "do the right thing" and remind her that she is NOT doing the right thing might backfire big time.
I am sure that the bio mom KNOWS this is her daughter's birthday - even clueless women remember things like this. It's been her choice to remain estranged from this child and her other children. There is nothing you can do to change her. And getting her to send a birthday card or make a call might just reinforce for your SD that the bio mom is not there the other 364 days a year.
If you have to make a phone call, make it to the therapist and find our how to proceed. Or, have her father make that call to get some objective guidance. You admit that you and he aren't sure if you want the bio mom to reach out or not - and if you are confused, it's likely that your SD is too, particularly as an adolescent who finds so much in life bewildering anyway.
Teen years are tough. Kids, especially girls, often feel rejected by peers, teachers, the world, etc. Don't highlight that she's been rejected by her bio mom.
If she brings it up, you can say "I am sure your mother is thinking of you today even though she is too troubled or too confused to be able to respond in the way that you would like." Then drop it. If she wants to talk, great. Listen. Then reassure her that she is a glorious child, a wonderful young woman, and she has her whole life in front of her. She cannot change her past, but she can direct her future and be the kind of person she thinks will be a benefit and a blessing to others. Her experience can be used to make her feel neglected or abandoned, or it can be used to make her a more compassionate and caring person. Of course, stress how proud you and her dad are of her, highlight a couple of key areas (don't go overboard), and make her day about the things she enjoys.