Mark Bell has a wonderful answer for the knot tables. I thought I would provide an answer for the census data. Using SnapPy, the current version of the OrientableCuspedCensus, which is a combination of the Callahan-Hildebrand-Weeks census, Morwen Thistlethwaite's 8-tetrahedral census and Ben Burton's 9 tetrahedral census, appears to have 77 2-bridge knots according the following computation. 

     CC = OrientableCuspedCensus(num_cusps=1)
     knotcount = 0
     for C in CC:
        if C.is_two_bridge():
                print C.identify(), C.is_two_bridge(), C.volume()
                knotcount = knotcount+1
     print knotcount


This function runs in the SnapPy application. Note: printing C.is_two_bridge() identifies the two bridge knot.  Note that copying the code and then typing '%paste' on the command line is the easiest way to run the code yourself.