From: St. Petersburg, Florida, USA
Actually its a One Day thing (supposing the "Day" equal turn and starts with Replay.
0. You are giving orders for the next turn, order the unit from Home Base A to Forward Base B (the transfer), and give it orders to fly a daylight mission to bomb X
1. Unit is exposed to whatever could happen to Forward Base B during the Single Night Phase (Naval bombardment/Night air bombing).
2. Still within the same turn resolution now follows the Morning Air phase - the unit will probably fly its assigned mission to bomb X (rolls, etc.)
3. Still within the same turn resolution now follows the Afternoon Air phase - the unit will probably wait this out (exceptions being CAP/Escort/Naval Attack/Naval Search/ASW which are flown on both AM/PM phases) and subjected to retaliation.
4. Turn ends. During the next order phase you move the unit from Forward Base B to Home Base A.
5. During another turn resolution the unit is already on Home Base A.
Thus in fact the unit is based on Forward Base B during a single day period - One Night Phase, AM Phase, PM Phase.
IRL it was similar - say Townsville to Port Moresby transfer happened during the evening to land at PM with the darkness approaching. Planes would be refueled, crew rested. Early morning next day they would probably be already in the air (so as no to be caught on ground) en route to target. Once back from the mission, they would land at PM, refuel and depart back to Townsville ASAP. This minimized risks of being on ground at Port Moresby AF, but resulted in Townsville-PM and PM-Rabaul-PM-Townsville time spent in the air during less than 24 hours!
Depending on the distance staged the air unit will either not fly in the morning phase and fly the assigned mission in the afternoon phase OR not fly at all and wait until the next day to execute the mission.