Don't wrap with plastic. TBIII needs air.
Soak the rawhide in water until fleshy. Could take 1/2hour to 2 hours, in the mean time, size your bow(thin covering of TBIII) and it will be dry by the time your rawhide is ready to glue on.
Take out the rawhide and put on a towel to wick away excess moisture.
Add copious amount of glue to the rawhide. (smooth side), and lay on.
I use masking tape to hold on every 3-5", I use a socket to get out airbubbles. I then wrap with ace bandage. I come back an hour later, and unwrap and work out the bubles again. I rewrap. I come back a few hours later again and work out bubbles and rewrap. AFter about 3 hours, you can remove all masking tape and use only ace bandage.