The port has become an alternative route into the UK and has been described locally as “a problem of the first order”.
Police have stopped 1,765 failed stowaways at the port so far this year – five times more than in all of 2016.
Tented encampments have grown up near the ferry terminal, under motorways and in abandoned properties.
Most of the migrants are Albanian, but they also include refugees fleeing Syria, Iraq and Afghanistan.
Every day port police are stopping migrants trying to sneak on to passenger ferries or into freight containers.
Officers have increased patrols, installed cameras and motion sensors and reinforced fences to stop the situation getting out of hand.
On Monday the Civil Guard caught 26 stowaways.
Many had tried to board Brittany Ferries’ vessels that sail three times a week to Portsmouth, carrying mainly passengers.
About 100 migrants, mostly young Albanian men, are living in tents just 300 yards from the terminal.
Brittany Ferries’ freight ship Pelican carries 100 containers twice weekly between Bilbao and Poole, Dorset.
The police use carbon dioxide sensors to find people hiding in containers.
Cars, caravans and lorries are also searched.
Migrants can be handed over to the National Police’s immigration department and expelled from Spain.
But many are not thrown out.
A Civil Guard lieutenant at the port said: “Sometimes they hide in the containers twice in a day.”
Bilbao, in northern Spain, became a focus for peoples-mugglers after the Jungle’s closure last autumn.
Brittany Ferries associate director Roberto Castilla said 66 migrants had been arrested in the UK after being caught on ferries from Bilbao.
Of those, 35 were sent back to Spain. Ferry firms are fined by the UK for every stowaway and must pay for flights back to Spain.
It is not known how many migrants successfully make the journey to the UK.