There is no quick and easy way to do it. Growing elements takes TIME to look good. Many hours of tweaking and tedious work for a couple seconds of animation. In fact, it took a good day or two just to animate all the growing elements from our Swan Lake DVD/Blu-ray motion menu template seen here:
It really depends on what you are working with. My advise (This saves myself time) is to take the full image into AE and mask the first branch, duplicate the layer, delete the mask, and draw the next branch. If it's a "blooming" object it's easiest to just make a whole bunch of traced leaves or other elements in AI and slap them in wherever you need them. Using Stroke is easier on the CPU from my own experiments to animate the "vines." Yet it still takes about two-three hours from the tracing on paper to getting the masked element to masking each individual item to animation. The really great thing is if you do in the highest resolution your CPU can handle you got an amazing animated flourish that can be used again and again in any size comp. Hope this helps!