Of course you want bumpless both ways - Auto to Manual and then Manual to Auto. It depends upon the controller...
With a GE or Siemens PLC my program turns on the Manual bit of the PID loop. When manual is on the manual setpoint is moved into the PID loop. When manual is switched off the PID loop takes off from there - naturally bumpless. Then when in Auto (not manual), the program moves the pid output to the Manual setpoint, making it bumpless the other way.