Green describes the general setup quite well.
Let's look a bit deeper into the issue of breaches of the hull, materials, and support, as well as protection from radiation and micrometeors.
we may want a magnetic field to ward off energetic particles, the way our own planet provides it. That, though, is not part of the current project, so we leave that aside.
While we could build a metallic bubble structure, and that would keep a lot of radiation out, it would also mean we would block the view, as well as any incoming light, which would otherwise be uite handy, givn that humans rely a lot on sight for almost anything we do.
So we may want a transparent shell for our habitat. After all, what would be the point of roaming the surface if it still felt like travelling in tunnels and caves? So transparent it must be.
We will use a multi-layered apploach, where the entire shell of every bubble is created from layers of the same polymers we use today for UV-blocking sunglasses. As a nice side effect, we can even have different colours for the individual bubbles, which gives beautiful artistic effects. We pay a fortune for that project, so it might as well be beautiful.
Obviously, a single layer of plastic won't withstand the impact of a very fast stone. So we have multiple layers, and inbetween the layers we inject a polymer gel. The pressure of the gel strengthens the structure and helps maintain the bubble's shape. also the gel not only slows down any impacting object, it also hardens when in contact with the atmosphere, or when illuminated with ultraviolet radiation. This way, not only are micrometeorites slowed down significantly while travelling through the layers of the bubble, often slowed down enough to be contained in the lower layers, the gel also works at closing small punctures automatically, resulting in next-to-zero loss of atmosphere.
The setup from a large number of individual bubbles provides additional protection, even if a larger breach should occur, much as described in Green's answer above.
Walling off each of the sections is an option. It can be done, but it would me more beautiful to have large open surfaces, so let's look how that can be provided.
Resting the bubbles on six points each, the corners of the proposed hexagons, should suffice. The pressure both inside the membrane structure as under the bubbles will take care of holding things up. The pillars will mostly provide anchoring points, and make sure the whole structure doesn't wobble around.
Expect spacing the pillars betwenn 100 and 500 meters apart.
The pressure inside the membrane system is provided from the ground, through tubes or hoses inside the pillars. Sensors will notice a drop in pressure, thus indicating a larger breach. Upon detection, around the borders of the section in question airbag-like structures can be inflated quickly, to wall off the compromised section.
Fear of a complete loss of atmosphere should be unjustified. A pressure of 1 bar is not that much, and air takes time to escape through any hole, so even a complete loss of several sectors will do less damage to the atmosphere than it will do tho the asteroid itself. The drop of pressure may be noticeable, even unpleasant, but never life threatening, unless one found oneself in the sector that got hit, but even there the damage from the impact will most likely pose a much bigger threat than the loss of atmospheric pressure.