[Shirazmn]

I'm in a similar situation and about the same size boobs. I ordered a couple of bras and when the wife saw the charge on the card got upset. I explained that my boobs jiggle when I walk and I get self-conscious. Also getting pain from excessive movement of which she could relate.  It took her a couple weeks to warm up to the idea but after I  had her stand behind me and actually grope my boobs, she's finally on board. 
 I have to admit that I really enjoy wearing a bra!

yea, this has been a very slow process.  complaining about shirts rubbing on my nipples.  Finding shirts where my nipples don't show.  If she found one of my bras I don't think it would go as well.  I really needed it to be her idea.

Agreed! It should definitely be her idea.If you are willing to wait a few months, next Summer you could suggest that the vests are too hot to wear in the heath and get her to suggest sports bras (that are essentially shorter vests). 
If that goes through, make a few comments about how good the light padding feels when it protects you nipples further.

From there, the following Winter when you wear more layers, you could progress into t-shirts bras, which are lightly padded "actual" bras.

Take it easy. If you raise the bet too soon it could cost you everything.