The ship docked at Catania, in Sicily, where the migrants will be handed over to the Italian authorities.
Bulwark, which has been on a search and rescue mission in the area for the past month, rescued the migrants on Sunday.
Captain Nick Cooke-Priest said the people traffickers were committing acts "tantamount to murder".
BBC defence correspondent Jonathan Beale, who was on board Bulwark during the rescue, said a small, wooden vessel had been packed with about 400 people.
There also had been two rubber dinghies, each carrying about 100 people, trying to get to Europe from Libya.
"The fact that many didn't even have life jackets was another reminder that the gangs who trafficked them had little regard for their lives," he said.
He added that five of the men rescued were going to be questioned by Italian police about possible links to the smuggling gangs.
The BBC's Clive Myrie, who is in Catania, said it would take several hours to disembark all the migrants from HMS Bulwark.
"They are exhausted, some are traumatised and several are pregnant, so it is going to take a long time," he said.
"Once on dry land, they are taken to reception centres across the country but it could be years before they receive papers saying they can live and work freely in Italy.
"As for HMS Bulwark, in the early hours it will head out to sea on the lookout for more migrant boats."
The ship's captain said Sunday was a "complex" day of seven search and rescue operations, and a "huge success".
"Normally we would be putting Royal Marines and sailors on to hostile shores," he told the BBC.
"The only difference with what we were doing yesterday was we weren't putting my own people into harm's way. We were actually taking survivors out of their harm's way and recovering them to HMS Bulwark."
He added the traffickers who sent "women, children, the old, young, pregnant out on a very perilous journey in unseaworthy vessels" were a "scourge".
The UK government dispatched the ship amid a rise in the number of people dying while trying to reach Europe.
The latest rescue brings the total number of individuals saved by HMS Bulwark so far to more than 2,700. Last week, Bulwark rescued 747 people from boats off Libya's coast.
The 19,000-tonne assault ship is one of numerous European vessels on rescue patrol in the Mediterranean.
They are patrolling about 70,000 sq miles of the central Mediterranean, looking for people including those fleeing Africa and trying to get to Europe.
It is estimated more than 1,600 people have drowned so far this year trying to make the dangerous crossing.

Leiua has played 30 games for Wasps since joining them from Super Rugby side Hurricanes in April 2014.
The 28-year-old, who can also play on the wing, has scored two tries in 11 Test appearances for Samoa.
"He's a robust midfielder who can play in a number of positions in the backline," Bristol head coach Mark Tainton told the club website.
"Alapati was a standout performer for the Hurricanes in Super Rugby and made a similar impact in his first season with Wasps - he will be a fantastic addition to the Bristol Rugby squad."
Bristol are currently bottom of the Premiership table, one point behind 11th-placed Worcester with nine games left to play this season.
Royal Navy warship HMS Bulwark has arrived in an Italian port, carrying 1,200 migrants rescued from the Mediterranean Sea.
[NEXT_CONCEPT]
Bristol Rugby have signed Wasps' Samoa international centre Alapati Leiua in a deal to start from next season.