Rudd joined the glycobiology institute at the University of Oxford in 1985. At the time, it was difficult for women scientists to secure jobs as academic personnel, and Rudd joined as a glass washer. She learned how to work with glycoproteins and large sugars and eventually completed a doctorate on glycoforms at the Open University in 1995. Rudd moved to the Scripps Research institute, and held a visiting position at the Ben-Gurion University of the Negev. She commercialised her work on liquid chromatography–mass spectrometry (LCMS) with Waters Corporation.
Rudd has worked to miniaturise technologies for glycol analysis. For example, she has used genome-wide association studies (GWAS) to link individual genomes to their serum glycome and individual proteins. She moved to University College Dublin in 2006, where was made head of the Dublin-Oxford glycobiology laboratory research group. She opened the National Institute for Bioprocessing Research and Training (NIBRT), where she developed new processes for protein glycosylation in an attempt to characterise recombinant protein drugs.