I am 6' tall and have B cup breasts. I am intersex and gender fluid, and depending of the situation I go as a guy, but most of the time I am woman. If used a tight fitting sports bra, and loose fitting shirts, specifically those with breast pockets, I can still hide my boobs pretty well, and I can wear such an outfit all day long.
The only thing you have to be aware of, is the fact that estrogen tends to feminize your face (different fat deposition), with some people earlier, others are later.
I think that I would have difficulties to hide my breasts once they would be a C cup, unless I would wear a wide sweatshirt.
Again mileage on estrogen varies, some people never get ny real breast development, others have their breasts growing pretty fast and larger big. I seem to be in he middle field, and can feel the growing pain, but not see much advancement over what I have currently.
And that is another thing, once your breasts start to grow, they get so sensitive against touch, and hurt badly when touched hat yo better learn to watch out for the girls if you don't want to be in constant pain. I found that a padded bra woks best for keeping the pain down to a minimum!