I would be hesitant to rig up a sleeping bag uq. It can be done, but it's trickier than you might think, and the margin for error can be pretty small if the temperatures are low. At the very least, I would do a test hang in your backyard with your intended set up and put it to the test. That way, you can bail out if it's 3am and that "insignificant" gap underneath you is causing some serious CBS! I know plenty of people prefer the ENO double as their main hammock, so I really think an uq would be a smarter purchase.
The WM blue tarp will work just fine if you don't mind the added space and weight in your pack. Make sure to set that up too to make sure you have al the lines and hardware you need and that you can get a good pitch. I might even upgrade this before the hammock too because you don't really realize how big and heavy those WM tarps are until you buy a "big" tarp like my Warbonnet BMJ and are certain the box it came in is empty since there's NO WAY a tarp that big could fit in a box that small and light!
Oh, last thing. Are you using the ENO SlapStraps for your suspension? Those things will sag on you overnight and make fine tuning your sag impossible.
I don't want to talk you out of the BB. It's a fantastic hammock. But right now, the hammock's not your weak link. Feel free to PM me if you have any questions.