Before checking for turned taper, I check for perpendicularity of the cross slide travel to the spindle axis. If the travel isn't perpendicular, you will cut a dome or a dish depending upon which way the the misalignment runs. Since the carriage isn't moving on the ways, a twist in the bed will have minimal effect on this cut. On my lathe the only way to adjust this is to adjust the headstock.
I check for proper alignment by mounting a boss on my faceplate several inches from the center. I set up a dial or test indicator on the cross slide and rotate the faceplate so the boss is to the front and horizontal with the spindle axis and adjust the indicator to intersect the boss with the cross slide retracted. I zero my indicator and rotate the faceplate with the boss to the rear and horizontal and move the cross slide so the indicator again intersects the boss.. If the reading is zero, the cross slide is perpendicular with the spindle axis. If not, the difference divided by the separation between the two measurement points is the amount of taper. To ensure hitting the same point on the boss , I place a small marker dot on the boss.
Once this is done, I next adjust turned taper, checking by Rollie's Dad's method or by the two collar test. Finally, I adjust my tailstock using a modification of Rollie's Dad's method or by the two collar test.