The only "problem" with starting a pump dry is that the impeller can strike the wear ring and damage one, the other, or both. The wear rind is the "seal" that keeps high-pressure water in back of your impeller from chasing arround to the front, ruining efficiency and drive thrust. If the wear ring is steel or bronze (I had a bronze once), the impeller will get damaged (assuming an aluminum inpeller) causing both blowby AND cavitation possibly. If the wear ring is the Polyurethane one I have fron Duane HTP, it will get hot immediately and melt (ruining it) as mine is a "contact fit" slightly brushing the impeller, closer fit than metal rings.
Similar damage happens from sand ingestion so be careful there too.
The bearings are lubed with grease (thrust in front) and 90-wt (bowl bearing) so a dry run won't bother them. Opinion on dry runs is mixed in here, some think it is OK, some run with a hose for lube, some think it is bad. Folks with rings like mine were told by it's inventor to never run them dry unless you disconect the drive from the engine, that a hose is insuficient in my app.