Maybe it's not so much a thing of sheer reflexes but also one of acceleration. Emily probably catapulted backwards at a speed greater than the one she had while approaching the hit, and we could think that Bubbles' armor isn't tied to any robo-nerves so her reaction would be determined by visual input.
Considering that Emily was already on a downward trajectory when hitting Bubbles and gravity, Emily hit the ground about .3 seconds after she hit Bubbles. If Emily was flung backwards at more than 5m/s, that means that she'd have moved over 1.5m backwards before hitting the ground. And she probably was, since Emily is 6'4" iirc and she's shown completely extended before hitting the ground. Bubbles was standing still, slightly arced backwards. Even if she took just 10ns to see and process all the information and decide to move forwards, she still only had .3 seconds to start running, move forward about 2m, bend over and grab Emily mid-air, preferrably in a way that didn't imply breaking her in half.
There might be some inaccuracies as all this calculation is off the top of my head and I'm not taking air friction into consideration, but everything seems to indicate that Bubbles would've need some really powerful servos to perform that stunt (and she tried even).
Note: Even if Emily was at the peak of her jump (which I had to assume she wasn't given the previous frame), fall time wouldn't have exceeded .5 seconds at any rate, unless she was capable of jumping over Bubbles.