In a Two-Headed Giant game, life gained by your teammate won't cause Sanguine Bond's ability to trigger, even though it caused your team's life total to increase.

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Sanguine Bond's ability will trigger twice and you may choose a different opponent for each trigger. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

If an ability triggers whenever an opponent loses life and causes you to gain life, such as the ability of Exquisite Blood, this will loop until either you win the game or a player takes an action to break the loop. If neither of these happen, the game ends in a draw.

If you gain an amount of life "for each" of something, that life is gained as one event and Sanguine Bond's ability triggers only once.

Sanguine Bond's ability triggers just once for each life-gaining event, whether it's 1 life from Soul Warden or 8 life from Tendrils of Corruption.