I have a pair of zip up pouches (came in my flight bag but are far more useful for this).
In one I have nappies, wipes, fold up change mat, nappy sacks, cream.
In the other I have a bib and a change of clothes.
If we are going out for any length of time, particularly away from home, I chuck both pouches into my change bag. Said change bag also tends to have things like DDs juice cup, snack selection, reins, receipts, and my purse, filofax, phone, random tampons and other crap lurking in it.
If we are only going out for a couple of hours, or just in the local area I tend to sling the nappy pouch in the basket under the buggy, and my purse in the pocket on the back with her cup and a snack. DD is now 16 months and rarely needs a change of clothes so I only take them when I know I won't be able to just nip home if necessary.
Lately if we are only popping out for an hour I've started going change bag commando and just taking a cup and my purse. Does feel a little risky though hehehe!