I just spent a week using my BMBHing a bicycle tour of the Hudson Valley (Albany NY to NYC). I found suitable sites to hang the hammock for all but one night. The Therm-a-rest NEOAIR makes a big difference in flattening the sleeping surface but does have drawbacks. The NEOAIR is just too warm for hot summer nights! Also, stability decreases when you pump-up the neo-air. Very manageable but you have to really be aware of what you are doing.
I wonder if a bridge hammock could be designed specifically for use with a NEOAIR (or similar pad)? If so, it would need to be deeper and the sidewalls would need some sort of wind block/insulation.
Tree straps turned out to be my biggest problem (stretch). JRB's Tri-glides work well but are not as easy to use as I Like. At least J RB's straps don't stretch and so wound up being my go-to straps for this outing.
Whoopee slings are one modification I made to the BMBH and they really improved ease of use. Highly recommend this solution.
I used a Chinook 12 x 9.6 tarp and it worked perfect for the BMBH and was within my budget. The seams on the tarp come presealed with some sort of tape. I was lucky, it did not rain on the ride so I did not really experience the full use of the tarp.
One item that worked out well was a diver's changing mat. Divers use it on the beach when they are changing into/out of their scuba gear. It is woven plastic, keeps the dirt down and feet clean.
Overall, I am very happy with the BMBH and NEOAIR combination. Can't wait until it gets colder to see how well the combination works.
I have attached some photos of the hammock in use. You can also see in the photos my bike (a recumbent tricycle) and other gear including tarp and diver's mat.