Wow...I live in a very similar area (in Minnesota, not Arizona). Lots of fast food restaurants, Walgreens, Kmart, grocery store, bars and a bus station all within a mile or so from my apartment. I also live near a main street for the city bus. It isn't unusual AT ALL to see people wheeling luggage around. Not common, but it wouldn't stand out, either. The bus has a departure that heads out at 7 am or something, so someone walking around with a suitcase at 6 am probably wouldn't raise any eyebrows.
It IS weird that she went to Walgreens to get the bleach instead of the grocery store, but all of us have weird shopping patterns. I go to Kmart to buy Tide instead of the grocery store, even though the grocery store is next to the laundromat. It's just my habit. It doesn't have to make sense.