are you doing this as a one way trip or a loop? Like the others said.. getting onto the bike path would be the easiest way from prov to Bristol about 15 mi flat. Then you'd take 114 over mt hope (which can be quite busy and an uphill start or you can take the RIPTA bus across), then take 114 or 138 through portsmouth and middletown.. both equally busy.. but if you look at a map or google then you can find side streets that go parallel that will be less crazy.