In my opinion there is no single method to purify and isolate bioactive peptide(s). You will need to use a combination of several chromatographic methods. Bioactive peptides are usually low molecular weight peptides so after hydrolysis, you need to inactive the enzyme and then centrifuge and filter the mixture to separate the soluble peptides from the indigested material. You can start with size exclusion chromatography (or ultra-filtration membranes) to fractionate your peptide mixture depending on the molecular size. Then you need to assay each fraction for bioactivity and once you determine the potent fraction you can further fractionate it based on polarity (reversed-phase chromatography), charges (ion exchange chromatography), affinity, hydrophobicity, etc.
You should first separate the whey fraction of the milk through a ultra filter. Then you should do HPLC analysis and the fractions separated should be analyzed for the bio-activity that you are looking for. You should then re-fractionate the fractions with higher bio-activity. You should do this several times and after few HPLC runs you can separate peptide fractions that appears in the chromatographs. Then you can use MS/MS analysis or peptide sequencer to identify the amino acid sequence of the specific peptides.
First you need a sensitive and quantitative measuring method of the particular bioactive compound. Than you may use any (or all) of the mentioned methods for fractionation of the starting material.