Without going into the details of how to exactly when to control making the switch(microprocessor choice, etc.), your USB cable consists of 4 wires, +5v, d+(data positive), d-(data negative) and ground. Depending on what device A is, if it has any sort of "bootup" time, you may not want to use the power lines as your "switch". What I would recommend is a DPST relay(something like
this) connected to the d+ and d- lines on the USB cable. Then, through your choice of control methods, turn the relay "on" at the end of that initial 30 second period, thereby connecting d+ and d- between devices A and B. You may have to experiment with the timing for when to switch the relay on, as there may be a delay after the devices are connected before they each realize that the other is there.
Hopefully this helps somewhat, I can provide more details if you are interested.