I don't believe that pushing for your transgender child to participate in women's sports is going to relieve her of bullying and the accompanying mental anguish. On the contrary.
Millions upon millions of kids, straight, gay, and otherwise go through life perfectly fine without ever or barely participating in organized sports. Even if I didn't believe that it was fundamentally unfair for transgender females to compete against biological females in strength related sporting events, the last direction I'd be pushing for my transgender daughter is towards anything that is going to subject her to more scrutiny, bias, and degradation. If it's that important to their mental and physical well being, then they can still compete against the boys. Last I checked, people aren't losing their shat over that.