Is there a bad time of day when the zika-carrying mosquitoes come out?

Doesn't matter: As yet there is no mosquito transmission of Zika in the US. That could change. If and when it happens, we can expect it primarily in warm climates in the SE, like Florida, other Gulf states, and the Carolinas. If so, time of day won't be an important issue. Even if some mosquito carriers at most active at different times, all-day protection will be necessary, especially for pregnant women.

All day long: The mosquitoes that transmit Zika virus (as well as dengue fever and chikungunya) are Aedes mosquitoes. Unlike some mosquitoes, Aedes bite all day long. They tend to stay close to human dwellings and will even live indoors, especially in buildings with no screens or air conditioning. They are found throughout the world, especially in tropical and subtropical areas, including the southeastern US.

Often in daytime: The Aedes mosquitoes that spread Zika mostly bite during the daytime, both indoors and outdoors. They are the same mosquitoes that spread dengue and chikunguyna.