I just checked my Rod Maker magazine. Antti Kymalainen's article on birch bark handles. What he says when you glue them together, do not glue more than 20 rings together at a time. Use a slow cure epoxy. BTW, lube up your bolt/all thread with pariffin so the epoxy doesn't adhere to it. Turn each ring 90? from the last one. Grain going N/S next ring E/W. After the 20th, put a washer on top and a nut. Tighten until the excess glue is squeezed out. Make sure the washer is larger than the rings too. Fender washers would work good.
After you glued all your 20 ring packets together, glue those together as one.
Good luck on your handle. I'd love to build one, but where I live, it's hard to find birch trees.

RTJ