Howdy Holten, As others have noted 7" is plenty long. The finer you shred it the smoother your backing will be. The backing can be applied in several ways. The easiest for beginners is probably applying fairly small bundles in what a brick layer would call a "running bond". Individual bundles are butted end to end ( let any tapered fibers overlap). But columns are staggered so the seams to not line up. The second layer is applied so the seams do not align with the under laying seams.
Some people advocate titebond glues for sinewing, but collagen glues are traditional and work better ( in my opinion.) Rabbit skin glue is high quality and available from most art supply stores (it is used for sizing canvas before painting.) Making your own glue from scraps of sinew & / or rawhide is simple, especially if you have a crock pot. In the US, most upper end woodworking stores/ catalogues carry hide glue. And of course commercial gelatin (Knox®) works well too.
As an aside hide glue works well for gluing wood and has a long and successful history. It's just fussier to use than Titebound type glues and not as water resistant.
Don't worry about your bow falling apart in wet weather, though. I've had some failures, where I've tried to recover and reuse the sinew. It takes hours of soaking in warm water to loosen the sinew. If the sinew is covered with snake skin or birch bark it takes days of soaking!
As mentioned earlier, I've had some failures when making really short bows 48" and 29" draw), but it should be possible. At least one of my failures stemmed from not keeping things clean and dust free. Any oils or dust will decrease the strength of the bond. If you make your own glue, you will have to be careful to remove all grease from the glue ( the grease will form a layer on top of the gelled glue and can be scraped/ rinsed off.
Ron
