I had similar thoughts when I started. I was thinking that I wanted to hide them until I came out and until I thought I could pass reasonably well. I didn't want to look like a manladyfishbearthing and embarrass myself when I still look like a guy.
Right now, I'm at over 3 months and a week. I'm considering getting an underworks binder. I'm transitioning MTF, but I identify as genderqueer, and I want to be able to present as either gender, or as androgynous, so I think investing in a binder isn't such a bad thing.
Underworks has binders that FTMs use, and they've got much larger boobs than i'll probably ever have.