Our puberty more or less mirrors a cis girl's; how long you have breast buds depends on how long your breasts stay in that particular phase. I know girls who did for 2+ years without seeing much other growth, whereas my breast buds softened and blended into the surrounding breast tissue around the end of the first year.
As for how long it takes, everything I've seen suggest that it's the same as a teenage cis girl there too : some develop practically overnight, some can take up to 10 years, but in the end you get what you get. (I started on a very, very low dose and still had immediate, fast growth. I was a 42C by four months in. However, it looks as though my breasts are also almost done growing at nearly 5 years on HRT, while other women continue for several years more.) There's no indication that any amount of estrogen past what the body needs does much of anything except be excreted back out.