I don't know what's more absurd: asking that question of a senior partner or using a text message to do it.
A word of advice: If you're even thinking of asking the question -- that is, if you're not already noticing braless women in your workplace -- don't ask the question -- just figure out how to go braless without it showing. Camisoles with lycra content, jackets, layers -- there are many tricks. Don't forget nippies!
If none of the various tricks work to keep people from noticing that you are braless, you shouldn't go braless even in a workplace where you can tell women are going braless.