Hello:
I am laying a bamboo floor using 3 3/4" x 5/8" x 37" planks. They will go over a 5/8" plywood subfloor over a heated crawl space. The width of the two adjoining rooms they will be laid in is about 40'. I plan to start in the middle using a slip tongue and laying in both directions. My question is - Do I need to leave a 1/16" expansion space every 4' over the 40' width ? and secondly, what is a proper sized nail or staple for this type of wood and plank size. Hope you can help, Thanks.

As long as there are no drastic changes in humidity levels inside the home, you should be fine with ½" of expansion space. The floor is going to buckle in the middle before it takes up the expansion space, if a unfortunate flood happens.