Most folks will advise putting your tarp in a separate bag to allow for hammock setup under cover in case you get rained on, but your use will ultimately determine the method you employ. Good news is, there is no wrong answer. Since I'm in the deep dark swamps of South GA, we have "Zombie Skeeters" that do not fear DEET. I have my ENO Guardian and Doublenest assembled and wrapped up in snakeskins and stored inside a waterproof silnylon bag. Quick deploy and jump in.
When I get my tarp, I'll have it in mesh snakeskins and it'll be in its own breathable bag, in case I'm forced to put it up wet. There are other "sag' issues with connecting a tarp directly to the hammock, but I'll let the experts that actually HAVE tarps speak more intelligently on that subject...
If you manage a method of storing it as one "semi-assembled" unit, by all means please post it.