Bunny hops can be done without clipless pedals or toe clips. Kind of a crud video, but here's an example of how to do it on a BMX with flat pedals. Basic mechanics are the same whether you're on an MTB, road, or BMX. Bring up the front, then push it down fast enough to bring the rear up.
Better to learn without toe clips or clipless, anyway. You won't learn bad habits.