The Puente Colgante is located just north of Bilbao, not far from the motorway. I visited it from the Portugalete side. It was quite difficult to find a parking spot close by. Eventually, I decided to drive on for a while (farther up north), until traffic got less dense. There's a boulevard along the river that you can follow back on foot. The bridge actually is right in the center of Portugalete.
As others have noticed: the bridge bears a strong resemblance to the Eiffel Tower. It keeps attracting your view. It is grand and lean. The gondola that hangs and moves underneath looks like a little boat that is pulled back and forth.
Since 1999, the pillars of the bridge on both sides have lifts installed. These will take you up 50 meters, from where you can walk over the bridge's platform. At first instance, it looked like an interesting thing to do here. So I bought a ticket to the lift for 5 EUR. I got weak knees however when I looked up from below: the bridge looks so thin and scary! I entered the lift, but on the way up I told myself that I would go back down with the same lift immediately. I think it scared me because the construction is very 'open': you can see right through everything, so you also see all the depth and height.
Arriving at the top, the feeling wasn't so bad anymore. They have the upper platform totally encaged, and you cannot look down below your feet. I even started enjoying it! One can walk all the way to the other side of the bridge, to Getxo. When a gondola is passing underneath, you can see the cables rolling and feel the construction trembling.
In all, I found it a worthwhile WHS to visit. If you're really afraid of heights you can always take the gondola to the other side!