Some more ideas/suggestions. The following are what I wear at work on a daily basis. At work I wear either navy or black t shirts (slim fit but not tight, obviously) since I need to be able to demonstrate exercises and stretches whenever necessary and it helps patients/clients to be able to see how I am moving or the position of my body. I don't want bra lines or my breasts protruding in an obvious fashion, especially when meeting new patients. I typically wear a shape-wear top over my sports bra to conceal the line of the band, but you won't have to worry about that since you won't have anyone watching you move in such a specific way.
http://www.amazon.com/gp/product/B00JCC4X1E?psc=1&redirect=true&ref_=oh_aui_detailpage_o05_s00
http://www.amazon.com/gp/product/B00DPIG0XK?psc=1&redirect=true&ref_=oh_aui_detailpage_o09_s00
http://www.amazon.com/gp/product/B001KWD874?psc=1&redirect=true&ref_=oh_aui_detailpage_o01_s00
The first two are my go-to sports bras that I wear daily, out and about in the world and at work. I find I can wear loose t shirts or regular collared shirts without feeling like anything is obvious. I do think the XU bra like many high impact compression bras is a bit thick to wear solo under slim fit t shirts. The line of the straps definitely shows but it would probably work under scrubs. The underarmor bras will definitely work depending on the size of your breasts. I will even wear these to yoga class under a sleevless muscle shirt (it's hot yoga after all.)
The men's compression shirts I recently got because the price for three was good (like the price of a single decent bra!) and my breasts are down to a perky A from a full B (since I have been off everything for 6+ weeks and before that on severely reduced levels for a month or so before stopping everything.) from what I can tell trying these on, it looks like I can wear just these under loose fitting shirts and possibly even at work where I have to be more careful.
I tried t shirt bras way back when, but they are designed to accentuate a woman's breasts while keeping the nipples from appearing erect (frankly a problem I DO have and why I don't go bra less outside my home--my nipples announce themselves pretty much all the time, LOL.) Hence, the padded and molded cups. For me, they hid nothing except my large nipples.