Downtown Carrboro is about 2 or 2.5 miles from Southern Village, depending on where you live in the village. You could ride your bike there but some of the route is not great, and it is hilly in parts. My husband has done it - not sure how long it took him. I'm guessing about 20 minutes or so. Otherwise, if you want to ride your bike outside the village, you can do the Fan Branch to Morgan Creek Trail, but that's short. And I guess you could go to Walmart but that's on the road and not fun.
I used to be a pretty big bike rider, but I lived in a grid type city without too many hills, so I found it a lot more bicycle friendly, plus there was a 44-mile bike trail outside my door. :-) I haven't biked too much since I moved here. I am a huge walker and basically walk throughout Southern Village, on the Fan Branch Trail or to/around Southern Community Park. But anywhere else I want to go, I drive.
We rarely take the bus, as I don't find it very convenient or frequent.