Do we expect life to develop only in certain regions of the galaxy? If I understand correctly, the Earth lies in an area of the galaxy - the "local bubble" - that is relatively free of dust and gases and where no new stars are being born.

What is the current theory on the relation between life on Earth and this location? Or in other words: Would we expect life to exist anywhere in the galaxy, e.g. also inside some nebula, or only in specific areas, and how are they characterised?
There's a short answer here and a long answer.

Short Answer: It isn't special.

Long Answer: Yes and No.

The Local Bubble really isn't so special with regards to where it's placed in the galaxy. Location-wise, it's perched on the inner edge of the Orion Arm, one of the Milky Way's spiral arms. The Orion Arm, too, isn't incredibly special. It's relatively small - it's often referred to as the "Orion Spur" - and near 1/4 of the way out from the galactic center. Not too far away, but not too near. The donut-shaped area 4,000-10,000 parsecs out from the galactic center is, however, sometimes called the Galactic Habitable Zone. In theory. life as we know it could exist quite nicely any where in this area (I should note that the scientific community is divided on whether the Zone is important, with some saying that it is arbitrary).

But let's dive in deeper. Actually, we're in a decent spot in the "Arm." We're on the edge of it - not too near large groups of stars that could effect our system via gravity, or near any supernova candidates. And the "Arm" itself isn't really a spiral arm. It is, as I said earlier, more of a spur, or bulge. There aren't as many stars to watch out for. Also, we're near the corotation circle - i.e., we orbit the galaxy at such a distance that we move at a similar speed to the arms, reducing further the likelihood of crossing them. Is this necessary for life? Nope. But does it help? Oh, yes.

There are, of course, other factors that make this area a nice spot: No black holes nearby, gamma-ray bursts, etc. But could life survive elsewhere? Yep. These same characteristics can be found in many other places in the galaxy - and life can probably survive in even more dangerous spots.

By the way, I'd avoid using the term "nebula". Technically, we're not in one, or anywhere near one. The term can refer to a multitude of objects - planet-forming areas, "clouds" surrounding white dwarfs, and other rather photogenic places - none of which we inhabit.

I hope this helps.