Sizing the bow is an easy procedure, there is no need to "build up" layers. That's just unnecessary tom-foolery. 24 hours between coats means the initial coat is significantly dried out and will act as a barrier to the next layer. Every additional layer has to fully re-wet the prior layer if you want it to "soak in". Lightly sand with a coarser sandpaper (100-120 grit) parallel to the grain, brush on the warm hide glue and let it sit while you rehydrate the snake skins. A finely sanded surface provides less for the glue to grip onto, so a little roughness does not hurt. If you have used any oils or fats on the wood while heat treating, you are going to need to spend time scrubbing it out of the surface with Dawn dish soap and/or acetone. Oils and glues generally do not mix.
Water that is just warm to the touch will wet the skins in ten or 15 minutes. I use an old bath towel to lay out the skins, then I fold the towel over them and press to soak up excess surface moisture.
Paint the snake skins with your hide glue, and lay then on the limbs. They are gonna slide around like snot on a hot greasy skillet, so wrap them with a little rubber band on the handle end. Proceed to gently massage the air bubbles and any excess glue out toward the tips and off the edge of the bow.
Having a bucket of warm water with a tiny bit of dish soap and a bunch of extra towels is handy because you are gonna get sticky. When you find your hands getting gummed up, slosh them in the warm water and wipe dry, repeat as necessary.
Don't hurry, because that always messes things up. Slow is smooth, smooth is fast. If you find that the glue has gelled , don't worry. It has only gelled, not cured! A hair dryer on a low setting will un-gell the glue, and if you are afraid that it is drying out the snake skin, dab it with a damp sponge wetted in warm water.