I've only just started working, so I wondered this myself not long since!
For me it depends where I'm going and how discreet they want me to be. The outer layer is generally 'work clothes', pretty boring looking skirt, top and jacket. The bag I carry is very business-ish too. It stops awkward questions/looks in hotels from staff, and if I'm going to their home it won't get the neighbours talking. Underneath, however, either basque/stockings or babydoll/holdups. Just ask them what they want, really. They'll tell you!
I live at home, and they don't know. So I'll say I'm going to one of my friends houses or something, but they'd be highly suspicious if I went trotting off wearing a work suit. So I leave the house wearing the underwear, jogging bottoms, uggs and a hoodie (I'm not a total chav, it needs to be loose to avoid scragging up the underwear lol), and then swap that for the 'work clothes' in a carpark or somewhere equally glamourous. It takes a bit of planning, mostly stashing the work clothes and bag in my car earlier in the day, and doing my 'prozzie laundry' when nobody is in! One day I'll get caught out and be forced to do a job dressed as Vicky Pollard
Obviously, you want to keep your start-up costs as low as poss until you've done a couple of jobs. I've found Primark has a couple of decent looking sets for about ?10 each. Very ooh lala!