singleseater great post with good details about the logic of the air/ground sensing system. Regarding the bounced landing recovery FCTM suggest to change the config to Flaps 20 and follow normal go-around procedures.
It is NOT a go-around, leave the config. alone until ground clearance is assured.
From 777 Flight Crew Training Manual
Bounced Landing Recovery
Bounced Landing Recovery If the airplane should bounce, hold or re-establish a normal landing attitude and add thrust as necessary to control the rate of descent. Thrust need not be added for a shallow bounce or skip. When a high, hard bounce occurs,
initiate a go-around. Apply go-around thrust and
use normal go-around procedures. Do not retract the landing gear until a positive rate of climb is established because a second touchdown may occur during the go-around.
If higher than idle thrust is maintained through initial touchdown, the automatic speedbrake deployment may be disabled even when the speedbrakes are armed. This can result in a bounced landing.
If the speedbrakes started to extend on the initial touchdown, they will retract once the airplane becomes airborne again on a bounce, even if thrust is not increased. The speedbrakes must then be manually extended after the airplane returns to the runway.
And also
After Touchdown - Touch and Go
• Maintain runway alignment (PF)
• Flaps 20 (IP)
• Reset stabilizer trim (IP)
• Check speedbrakes down (IP)
• Thrust levers vertical (PF)
• Go-around thrust (PF)
• Rotate at Vref
• Climb Vref + 15-25