What is the name of a flower with a sugary bill?

The flower you're referring to is likely the "Nectarine" or "Nectar Flower," as these types of flowers produce sugary nectar that attracts pollinators. However, if you meant a specific flower known for its sugary traits, the "Hummingbird Sage" (Salvia spathacea) is also notable for its sweet nectar, which is particularly appealing to hummingbirds.