One of the challenges of hanging with a bridge hammock is that the spreader bars are wider at their customary height than a gathered end hammock typically is. A normal tarp has to be pitched higher and flatter above a bridge hammock than it is above a gathered end hammock, to avoid having its walls close in on the spreader bars.
A variety of solutions have been bandied about this last year, and I can now offer another, fresh back from field testing.
I bought lightweight tent poles from questoutfitters. 0.344" diameter nanolights. Two sections that make up one 36" pole weigh together 1.15 oz. The pair cost $5.15. I sewed in special tabs on the edge of my JRB 11'x10' tarp, that create a pocket for the pole end. The tabs are 20" on either side of the center pull-out tab. The new tabs both create a pocket for a pole end (by a little sewing on the grosgrain) and work as ordinary pull-out tabs as well.
A pole is slipped into opposing tabs on one end of the hammock.
Cord is tied to the tie-out loops, looped back and around the tree, and tensioned up on both ends. This creates a sort of ridge, so that the tarp slopes at a more shallow angle up high (and this angle is fixed) and then can slope at a sharper angle to bring the tarp sides down to give better side coverage to the hammock. Here's the result.
Even with a gathered end hammock this technique will create a bit more head-room. It's a keeper for me.