The flavour (meaty, vegetable, etc.) generally increases in intensity as the protein is broken down, eventually into small peptides and amino acids. Degradation of proteins can result in the formation of bitter peptides.
Some bitterness will usually be present at intermediate degrees of hydrolysis. Bitterness is believed to be caused by the presence of peptides of a certain size with terminal hydrophobic amino acids, see for instance Figure 1.
After hydrolysis with endoprotease, short peptides are formed. Some of these have terminal hydrophobic amino acids and are thus bitter peptides. Further hydrolysis with exopeptidases breaks down these bitter peptides.
The tendency to bitterness therefore depends not only on the degree of hydrolysis but also on the structure of the peptides produced. For example, casein will, when hydrolyzed with Alcalase, start to get bitter even at a degree of hydrolysis of 1%. The tendency to bitterness is reduced substantially when hydrolyzing casein with Protamex, and further reduced when using Flavourzyme.