I always have a bag with me while I'm out: it's a bit like a messenger bag, cross-shoulder type, and has compartments for everything I need, which includes water, sunglasses, wallet, car keys, and UCD. No problems there. When I'm in situ, at home or in the office, the UCD sits on my desk. No problems there either.
My UCD is a small but fat spiral-bound notebook, which I chose because the larger notebooks with fewer pages get loose and scrappy really quickly, and shed bits into my bag.
I'm a bit of an anomaly among women, I think, because I've always preferred wearing trousers (pockets!), I carry a big bag which holds all my stuff (never have to ask for a tissue or squint in the sunlight), and I wear sensible shoes. And I haven't worn pantihose in at least a decade.
It might sound flippant, but I really think that function is more important than form: I see no point in wearing uncomfortable or impractical clothes just to fit someone else's idea of what a woman should look like. Sure, I dress like a professional when I have to, but that doesn't include tight skirts, high heels, or hosiery. And it certainly doesn't include going bagless.