Unfortunately, I don't have a reliable formula.
I plane the backing bamboo to 1/8 inch in the middle tapering to 1/16 inch at the tips. Cut the back to shape before final planing to get the ends thin. The belly lams are also planed really thin and the core is just over 1/8 inch with no taper. For the core, I planed a natural bamboo slat to thickness , but flooring bamboo could be used. I also used a power lam made from jatoba about 3/16 inch and 2 inches or so past the fades.
I use a blow torch to blacken the belly lams after I get them planed flat, but not too thin. Then I leave them for a few days before final planing. Torching bamboo makes it cup towards the outside, so be careful planning. I find this lets you get them nice and thin as the crown flattens a bit.
The problem I had with the third bow is that I used osage for the core instead of bamboo and I didn't taper it, so it came out very heavy.
One thing I like about these bows is that they draw smoothly and are nearly silent. The burnt bamboo looks really cool too.
Good luck with your build and let me know how it turns out.
Dave.