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The incidents came while President Donald Trump was on a visit to Asia.
China has increased military and political pressure on Taiwan to accept its sovereignty claims, drawing anger from the democratically ruled island, which has repeatedly said it would not be bullied and has the right to international participation.
The Pentagon would not confirm which islands the B-52s flew by, but recent tensions have focused on the Spratly Islands.
The flights drew a protest from Beijing, which labelled them provocative.
The Albion was on its way to Ho Chi Minh City, where it docked on Monday following a deployment in and around Japan.
While similar exercises have been held in the South China Sea in the past, the combined display by four countries represents a fresh challenge to Beijing.
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