I did try to use a store carry-basket with the stroller... not looking furtive about my efforts helped also. At one time, I used 2 canes to get around, so I had to make do with pockets in some stores... guess it was obvious enough what I was doing that nobody every got het up about it, although maybe they kept an eye on me to make sure I was heading to the checkout line and not the door.
You're right; it's a short phase. Bet she loves getting out and seeing everything and everybody!
Sorry about the exploding at both ends... sometimes burp cloths are just totally inadequate.