If a mosquito bites one person can the same mosquito bite a second person?

Yes. A typical mosquito meal is 2-3µl of blood. It is only the female that bites as she needs the protein and other nutrients for egg production. It needs about a minute to feed and, if disturbed, will fly off to locate another feeding site to get a full meal. This could be the same person, or a different person. Because of this, a disease-infected mosquito can infect more than one person per feed.

Aedes aegypti will feed up to 3 times during her short 2-week lifetime.