I live in North Attleboro.
1A would probably be the best way from Norwood, but it doesn't go directly to Attleboro, it joins with Route 1 in Plainville, and than splits off again in South Attleboro. You could also take route 1 from Norwood, I know someone who has riden that route with traffic, but I wouldn't go that way unless my life depended on it.
I ride 1A from Wrentham center to where it joins route 1 in Plainville all the time, it's a pretty leisurely ride. There are a couple of spots that are tight, but for the most part you'd have plenty of room to ride.
There is one section of 1A in Norfolk that's a little spooky because it's where the state prison access area is located. No stopping and don't be picking up strangers!
I ride all over the area, including into franklin, wrentham, foxboro, and sharon, if you're going someplace specific in Attleboro, PM me the street name and I can give you a good route off of 1A.