Every rodmaker who has tried to cut pieces of a bamboo pole, stack and glue them, has countered various challenges. First: the glue does not hold very well, second: it is quite a tough stack to turn into shape and third: almost impossible to drill a centerhole without breaking the stack.
But no worries mate, here is a top tip for you, the easy way out.
First go to the nearest kitchen supply store or the housewares departement of the discount hall and find yourself a square-shaped chopping board made of bamboo.
Something like this.
Saw into pieces with the dimension desired to be enough after turning in lathe, and drill a hole into the center of each piece. Glue the bamboo blocks together with a round wooden stick. Select the diameter of the wooden stick and the center hole so that it is app. 1-2 mm larger than the diameter of your blank. Set the center woodstick even at the other end and leave a couple of centimeters visible at the other, for attaching to the lathe.
After drying put the stack into lathe and start turning into desired shape.
During turning, it is a good idea to test eg. Different waxes or other treatments before turning into final measures.
And after your reelseat is in final dimensions with the necessary grooves made to reel foot, the whole delicacy of this trick will be illuminated for you!
Drill the center hole open with the drill bit matching the diameter of your rod blank. There will be 0.5 to 1 mm. wood and glue left inside around the hole to keep the bamboo blocks together and the drilling won’t break the stack!
And the bamboo reel mount crowns the finest splitcane rods you have made!