I have a couple of dresses with similar necklines to this. I wear a strapless bra and have little or no side bra showing.
I have a top like this which I wear with a cami underneath - mine is see through and my tummy is not my best feature so I am more self conscious about showing that, than my bra:)
For casual summer dinners or lunches, BBQs etc I would totally show a little coloured bra or bandeau top, either matching or contrasting. I would not for work or a formal dinner or wedding. I would not choose a nude colour but either sharp white or teal or coral.