That is cute! Congratulations!
As for what to wear under it, I'd recommend a tank top or a cami. I don't think it would work over a long- or short-sleeved shirt -- unless, perhaps, that jacket is very loose. You could also try it over a dress, preferably sleeveless or strapless, as a coverup.
Or if you're feeling naughty -- and/or want to get noticed -- just wear a bra under it! Or a corset.
But really, try it and see what you think.
As for where to wear it, I doubt it would work for "business," casual or otherwise. But that really depends on your business, of course. Might work for casual, depending on what else you wore with it. Formal or clubbing sounds like a good bet.
And if it doesn't seem appropriate for the crowd you're with, you can always take it off.