When I first started training (which was not that long ago - less than a year. I'm a newbie!), it was just after the birth of my second child, whom I was breastfeeding. I would place absorbant cotton nursing pads in my sports bra before going to training to prevent any milk from staining my gi.
During ukemi practice one of my nursing pads flies out and lands right in front of another student, a childless guy who probably knows nothing about the woes of lactation. As nonchalantly as possible, I retrieve it, turn away briefly, stuff it back into my bra, and continue rolling.
I'm not positive he noticed, but if he did, I'd bet he's still wondering why that crazy beginner stuffs her bra for Aikido!