If the girls are starting to show, I wouldn't display them in any public space.
Use the ladies' room if you are presenting a female appearance, and the men's if you are presenting as male. Granted, that is problematic in some jurisdictions. It would still be my first choice unless accosted by the bathroom police.
I am very much part-time, but twice, when out in public as myself, I have used the ladies' room without raising any eyebrows. It's not about passability; it's about safety. No way in h*ll am I going into a men's room wearing a skirt, wig, and makeup.