Except for the time dilation; the transmission rate appears (in Ender's frame of reference) to be on the order of bits per second, even if transmitted in gigabits per second...
But not when the receiver is traveling at relativistic speeds. The transmission would appear instant to those in flight but the transmission from the planet bound ansible would be drawn out so that the computer on the receiving end wouldn't get the file at a bit-rate faster than it is able to process.