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.