I had thought that military crossbows were pretty much extinct in England at that time. Might the crossbow perhaps have belonged to a foreign soldier or be the personal possession of one of the officers? What would it have looked like - my guess is something like one of the Spanish Padre Island style bows, which we know were carried on Spanish galleons of the period. The bolts were a bit lighter than some of the medieval ones I've seen and that would fit with the smaller Spanish style bow. Who knows but it's fascinating to speculate!
Sorry I don't have a picture