i think you are just on about a regular ollie, no?
IMO a bunny hop = lifting both wheels off the ground simultaneously, which has it's own merits for changing lines and stuff like that
an ollie = lifting the front wheel first, followed by the rear and is the proper way to get off the ground because you can use different forces to get the bike higher. theotherjonv has it about right – unweight the front wheel and pull high up (the manualling part) and as the wheel is reaching its highest point stand up fast (jump) on the pedals (which are now higher than they are with both wheels on the ground) and pull up with the bar whilst rotating your wrists forward and pointing your toes down to grip the pedals and help you get the back wheel off the ground. you then need to concerntrate on bringing your rear wheel up as high as your front, which you do by bending your knees upwards and the bike comes up between your legs.
like with a skateboard ollie (which i can barely do) it takes a lot of practice but once you got it, you got it. extending the manual before the jump takes more time to learn and is a bit further on from ollieing.
btw, i don't call it an ollie; it's just jumping – but it is the best way to describe the proper technique…and it probably should be called an ollie rather than a bunnyhop!