The UK government sent the warship to aid search efforts in the Mediterranean amid a rise in the number of people dying while trying to reach Europe.
BBC defence correspondent Jonathan Beale said the ship was sailing south with around 12 other European vessels.
Last week, Bulwark rescued 747 people from boats off Libya's coast.
The ship is thought to have been involved in the rescue of around 1,700 migrants in the past month.
Our correspondent, who is on board the ship, said: "Bulwark, along with about a dozen other European vessels, is patrolling an area of about 70,000 square miles of the central Mediterranean - looking out for those migrants desperately fleeing Africa trying to get to Europe. "
It is likely the vessel will locate migrants in the next 48 hours and attempts will be made to rescue them, he added.
Estimates suggest more than 1,600 people have drowned so far this year trying to cross the Mediterranean.
Many are fleeing war in Libya, where Islamic State fighters are terrorising the population, fuelling instability.
Royal Navy warship HMS Bulwark is heading towards Libya after reports 14 vessels carrying migrants have left the country's coast.