What happens if Bridgestone stops making tires

Given that there's only one supplier of tires for the i3, does anyone ever worry about Bridgestone deciding to stop making these tires? Is that at all likely?

Not likely. I would think that when more of these are on the road other manufacturers will produce tires for them.
Right now they have a monopoly, why stop making them?

Nokian does make a winter tire for the i3 (the R2), so it's not a total monopoly. At less than 50K cars/year, and the fact most people don't put huge amounts of miles on the thing, and it's only been around since late 2013, while yes, some have had to replace tires, there is no huge market for them, yet. When there's a market, there will be people to fill it.

Bridgestone is the sole manufacturer of the very low rolling resistance tires on our Honda Insight of which fewer than 20,000 were built, yet Bridgestone continues to manufacture these tires. One difference is that other tires of the same size but higher rolling resistance are available. The last Insight was built 10 years ago, and far more i3's have been built, so I'm not worried about future tire availability.

I was chatting with my dad about this - he has a 1981 Delorean sitting in his garage. Evidently you can no longer buy tires for it that fit the original rims (although, there were only ever 9000 Deloreans made.) Modern day Delorean owners buy replacement rims with modern day tires that are close to the originals. That would be tricky on the i3 though, since fitting a wider tire would need a really shallow offset on the rim, and would stick out way past the fenders.

Things to think about if you intend to drive this car a really long time. Since it's aluminum and carbon fiber, it won't rust. The battery will need replacing, but it seems like BMW intends to offer upgraded batteries in the future. It's not impossible this car would last a very long time.

I done an Internet search recently to check the price of tyres. I was surprised to be given an option of manufacturer.

When I selected the other tyre it was a space saver tyre for Mercedes. Therefore, this size is not unique, but the actual tyre itself is.

I assume that if the tooling and moulds are available there is a possibility of other manufacturers supplying tyres once there is greater demand

I wouldn't be too sure on them stopping making a tyre. I have a strange size on my 1 series and they are run flats and they stopped making these for a period of time and I was off the road for a week while one was sourced. From their perspective, why manufacture something you don't sell to often when you could be making a more common size.