Practice, practice, practice?
Brian
One of the comments has a link to this article. Apparently that video is from a P&O cruise ship.
Yeah, that’s my comment, with the link I also posted here in #19. 
That was actually pretty fucking hilarious, I am crying.
Yes, maps of the UK tend to be deceptive because they usually stick Shetland in a little box in the corner, so you don’t realise that the islands are actually nearly halfway to Norway.
I thought it was worth asking. The Overseas Highway through the Florida keys is 127 miles long. It goes over a lot of islands, of course, but I was speculating before researching when I wrote the first post, and hey, maybe there’s a string of islands between Scotland and the Shetlands too. Guess not.
A friend and I had plans to go to Shetland once, but we gave it up when we saw the ticket price (air).
Not one that reaches all the way - as your research will have uncovered, there are the Orkneys, but it’s still quite a step from them to the Shetlands.
From the furthest north rock of the Orkneys to Fair Island, it is just under 30 miles. The distance from Fair Island to the nearest peninsula of the Shetlands is a similar distance. So, using the Orkneys to leapfrog (assuming bridges from Scotland, jumping around the islands), it is not exactly inconceivable. One could build pylons every ten miles (IIUC, the North Sea is mostly about 300’ deep) and have 20 floating platforms between each anchor point (having the bridge deck floating directly on the water sounds like a very bad idea).
But the first problem you encounter is that it is terrifically unpleasant to drive in a straight line for 30 miles, no one would want to use the bridges in the first place. Then, of course, you would be spending £50B for what, some sheep? Not going to happen.
Flights to Sumburgh do seem expensive* I’m sure the oil industry must have some effect on the prices. Mind you, Sullom Voe has an airport more-or-less dedicated to itself at Scatsa that runs shuttles for the oil workers from Aberdeen.
- Just checked, and I could fly out from Edinburgh tomorrow morning and return on Friday evening for £297. That’s not so bad for a short-notice flight I suppose, but I could get to Moscow and back on the same terms for £401.
Also note that the Overseas Highway actually only covers about 2/3 of the length of the actual Florida Keys archipelago. You can go all the way to the Dry Tortugas, but only by ferry.
Would the weather conditions make a difference? I guess that the water in Florida is a lot calmer than that between Orkney and Shetland, but I don’t really know.
And as you say, I suspect the demand wouldn’t justify the cost of the project, assuming it were technically possible.
I’m American, and driving 30 miles in a straight line doesn’t fash me. Doing it on a bridge resting mostly on floating platforms in the North Sea,* that* would fash me.
Agreed, I’m not seeing the fun.
I think the North Sea gets a fair bit of wave action, perhaps to the extreme of a two-story building. The first issue with that is having a floating road that, umm, floats. As in, up and down. The platform idea would reduce that effect somewhat, though one might be able to use some kind of pontoon, keel and section linkage scheme that would keep the sections in near-stable relative configuration, but that would be at least as expensive and difficult as using platforms.
The other issue is waves coming over the road surface. We have 3 surface-level floating bridges around here, two across a lake and one across a canal, but the wave action rarely exceeds three feet in those areas. I suppose some sort of wide verge grid could lie out away from the road by fifty or a hundred feet to keep the water in check (and act as a boat bumper).
The advantage to using platforms would be less restriction of sea traffic, depending on the bridge height. And the platforms could have round-abouts to keep drivers alert, allow for a change of heart and facilitate the mobility of law enforcement and emergency services.
OK…the question as to "how you get to the Shetlands"has been answered.
Now as to “why”-why would you want to go there…is its a happening place?
If you like short, cool summers without the actual Midnight Sun (though you do get all-night twilight at the solstice, and there’s an annual motorbike rally to celebrate it), hardly any daylight in winter, and an annual festival where they set light to a replica Viking longship, it’s just the ticket. That and a whole bunch of sheep.
The scenery, of course. 
Actually, I’m kidding, it does look rather picturesque in a rugged windswept sort of way.
Very exaggerated, I’d say.