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.

Lamborghini, which is owned by Volkswagen, said Italy had beaten a bid from Slovakia to build the car there.
Reports say the sports car maker received â‚¬90m ($98m; Â£64m) of tax breaks and other incentives from the government to produce the car in Italy.
Executives from Lamborghini joined the Italian Prime Minister Matteo Renzi at a signing ceremony in Rome.
The Urus SUV was unveiled as a concept car in 2012 and is expected to go on sale in 2018, with a planned production level of 3,000 cars a year.
That will more than double production at Lamborghini's factory near Bologna and is expected to create 500 jobs.
Other car markers have been attracted by the strong growth and in the SUV market.
In January, Jaguar Land Rover said it would build its first Jaguar SUV at its Solihull plant in the West Midlands.
And in February Rolls-Royce, owned by BMW, also announced plans to launch an SUV.

Jose Beltrame stood down a day after a high profile clash between police and suspected drug dealers in some of the city's best known neighbourhoods.
The shootout caused panic and forced shops to closed their doors on Monday.
Police say three men were killed and several arrested in the raid on the Pavao-Pavaozinho shantytown.
Dramatic footage posted online shows one of the suspected criminals falling off a mountain after being shot by police.
Pavao-Pavaozinho is built on the hills and granite mountains that divide the Copacabana, Ipanema and Lagoa neighbourhoods.
Mr Beltrame led a controversial programme that saw the occupation of dozens of Rio's favelas by police.
Residents initially welcomed the "pacification plan," and celebrated the arrest or escape of drug lords who controlled life in their communities.
But many eventually turned against the programme after accusing police of abusing their powers.
More than 260 favelas have been occupied since the programme was launched in 2010.
Rio's pacification programme was aimed at improving security and the rule of law in the run-up to Brazil's hosting of the football World Cup in 2014 and Rio's staging of the Olympics and Paralympics , which took place in August and September.
Rio residents say security has declined sharply since the end of the Games.
Mr Beltrame said the first phase of his "pacification programme" was to restore law and order in the city's poorest communities.
But he complained that there was no money for the second phase of the programme, which consisted of social improvements for residents, with the construction of schools and leisure facilities.
Brazil is facing a serious economic and political crisis and the state of Rio de Janeiro has been particularly hit by the downturn.
Royal Navy warship HMS Bulwark is heading towards Libya after reports 14 vessels carrying migrants have left the country's coast.
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Lamborghini confirmed the launch of a sports utility vehicle (SUV) and signed a deal to build the car in Italy.
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The head of security for the Brazilian state of Rio de Janeiro has resigned after nearly ten years in post following a recent rise in violence.