How much overlap should bypass doors have?
You want the doors to overlap a bit. You also want the two doors to be the same width so when they are slid all the way to one side or the other that they are even. 

A one inch overlap is about ideal so for a 48" finished opening each door would be 24.5 inches wide.

Two 24" doors would not overlap at all and would not stay fully engaged into the center guide on the floor.

Doors wider than 24.5" would work just fine but you loose access width when the doors are open.

My suggestion is that you may want to look at bi-fold doors. These would take four ~12" wide door panels. They work with one track at the top and eliminate the center guide on the floor. When open you get much much easier access to the closet than with bypass doors. Plus when closed the whole surface is flat. The only time I consider bypass doors is when mirrored doors are used to give a smaller room a more expansive look.