I believe that the bridge is still closed to all bike and pedestrian traffic. The bridge was designed to allow bikes, but the main access road (Route 138) no longer allows bikes. Work is supposedly going on to alleviate this, now that the old bridge has been demolished.
The RIDOT recommends that one use a bus to cross -- buses are equiped with bike racks. http://www.ripta.com/schedules/view.php
You might want to contact the Narragansett Bay Wheelmen to see what they suggest. http://www.nbwclub.org/
If time is not an issue, and the weather is nice, you could catch a ferry from Pt. Judith (Narragansett, RI) to Block Island, ride the island, and catch a return ferry to Newport.
This message was edited by rimike on 7-15-08 @ 7:51 PM