It looks real thick, and doesn't look that long for bison sinew. How long is it? As thick as it is, it will take a long time to dry, probably a couple days, as opposed to deer leg sinew that dries in a few hours. Couldn't tell ya anything more as I have never worked with bison sinew myself. But I wouldn't worry too much about it. If the guys said it's sinew, it probably is.
I do have one suggestion for ya. Take one piece and filet it open down the middle, and you might as well do the whole length so you end up with two halves. See what it's like in the middle. I would say it should be sort of shiny-white, semi glossy and not very greasy at all, as opposed to the outside. Shouldn't be any meat on it, if there is cut it off before it starts stinkin, also, because meat or fat will keep it feeling greasy. I have dealt with whitetail sinew before that stayed greasy forever, but it did dry ok. You just have to give it some time.
