I would argue against the prevailing view on here that it was EFP explosives, a precision missile strike, thermobaric bomb, special forces rigging the bridge, drone boats or similar high tech operation.
The first reason is the explosion itself. All of the above produce "clean" explosions where all of the reactive part of the bomb is consumed and you are left with smoke and inert debris. This explosion looks far dirtier. When the flash dims you see burning debris raining down. It looks very similar to an ammo depot exploding. For example this vid:
https://www.youtube.com/watch?v=NKJvcVM6jvE
The burning debris is likely propellant from tank/artillery shells, missiles, mortars, incendiary rounds, packaging and so on.
This entirely makes sense for an improvised truck bomb. There are huge quantities of these munitions moving through Crimea on their way to the front line. With the professionalism displayed by the Russian Army it doesn't stretch credulity that several pallets of these could make their way onto a truck especially if the bomber took a job related to logistics.
The second is the damage caused. Images of the underside of the bridge show it to be clean of charring or obvious blast damage. The piers are all intact and undamaged.
Look at the guard rails on the bridge. These are torn off or bent outwards. It is especially noticeable that they are completely missing on one span of the still intact side. This shows the blast must have occurred on top of the deck. If the explosion had taken place beneath the bridge deck the guard rail would have been shielded from damage by the deck.
I would speculate a truck bomb of several tons at least detonated on top of the deck. The blast wave travelled out in all directions. Up into the sky, horizontally outwards tearing off the guard rails and leaving the visible charring, and also downwards. The downwards force would act to bend the bridge deck into a banana shape which also puts the ends of the deck section under huge tension. (imagine holding up two pencils with a string tied between them then get someone to push down on the middle of the string. You feel the pencils being pulled towards the centre)
As all the deck sections are fixed together the force is transferred along until the weakest points are revealed or the blast runs out of power. This explains why in two places sections separated without signs of explosions. They were torn off by tension generated at the explosion site.
As for who orchestrated the attack I wouldn't like to speculate!