What respiratory diseases can be contracted while being bedridden?

Not being active for days on end can cause atelectasis, a condition where lung volume is reduced because you haven't been deep breathing.

Deep breathing is something we normally do without thinking about it, namely in the form is sighing. We usually sign ten times every hour when awake. When we're sleeping, we normally develop atelectasis. This corrects itself when we wake-up and stand, walk, sigh, etc... Deep breathing helps move secretions off our lungs so they can be moved out. Long periods (days, weeks) of being bedridden can cause bronchitis from the pooling secretions that get a chance to sit and grow in the lungs. If it keeps progressing, it can become pneumonia, probably bacterial in nature. A terrible episode of pneumonia can lead into Respiratory Distress Syndrome (RDS), which is life-threatening and would probably require mechanical ventilation with heavy antibiotic therapy to resolve.

I would say that Atelectasis would be most common in bedridden people, with pneumonia occuring when they are sick in addition to being bedridden. RDS could happen, but that would require the person to be severely ill beforehand (ie. late-AIDS, immunosuppressed).

Secondarily, because the person has not been active for days/weeks, their muscles in general could lose strength. This could cause difficulty breathing simply because they no longer have the mechanical power to breathe as they used to.

pneumonia is the most likely, and the most common

depends on how old you are - a common respitatory problem is pneumonia in older people but it is not a disease