I teach bounce recovery training in the 777 at my carrier.
1. Re-establish a "landing attitude" (~4 to 5 degrees pitch) to prepare for a possible second contact with the runway.
2. MANUALLY advance the thrust levers to GA thrust limit.
3. When airborne and climbing select TOGA
4. Command "Flaps 20"
5. (PM) calls positive rate off altimeter
6. (PF) call "Gear Up, check missed approach altitude"
7. 400 ft - check roll mode
8. 500 ft A/P on
9. 1000' - Speed up and clean up.
We emphasize not to retract the gear until you are sure you are climbing away from the runway. Hitting TOGA on the runway won't engage the auto throttles into G/A Thrust nor change your flight director pitch commands. However, once airborne and climbing, TOGA works fine. Of particular note is that a SINGLE PUSH of TOGA on any G/A commands a thrust that will give you "approximately 2000'/min VSI) for passenger comfort. With both engines running, you have to hit TOGA twice to get true G/A thrust.