Rob, I know a lot of guys use TBIII, and it could be ok. But when making a bow, I like to use a quality industrial strength glue. We go through all this work to make a bow, why not use a quality glue? I use Unibond800 and or Smooth On Epoxy. I have never had a failure with a glue up from limbs, to risers, to tip over lays.
However with risers, you need a longer gradual taper into the limbs as Bowjunkie explained above.