Snake a Tub Drain: Access Clog via Overflow Plate
Remove the overflow plate from the end of the tub; the stopper linkage will come out with it. Feed about 30 inches of cable down the overflow tube. Push forward while turning the hand crank. You'll feel resistance almost immediately, but keep cranking on the auger until the cable passes all the way through the P-trap that lies underneath the tub.
Retrieve the cable, then run several gallons of hot water down the drain.
Finally, replace the overflow plate and screen or pop-up drain.