How common is it to develop asthmas as an adult? What usually triggers this?

Not uncommon. Sometimes a viral infection can trigger this...or it is possible to develop seasonal or other allergies, even if they weren't there when younger. There are other lung conditions that can mimic asthma, so just be sure you've discussed this with your doctor or a pulmonologist or allergist.
Yes. It is possible. Some people show signs and symptoms as adults. We do not know exactly why and how this works.