Bifunctional enzyme that catalyzes the phosphorylation of pseudouridine to pseudouridine 5'-phosphate (PsiMP), and the reversible cleavage of pseudouridine 5'-phosphate to ribose 5-phosphate and uracil. Is involved in a pseudouridine degradation pathway. D-ribose 5-phosphate + uracil = H2O + psi-UMP ATP + pseudouridine = ADP + H(+) + psi-UMP In the N-terminal section; belongs to the pseudouridine-5'-phosphate glycosidase family. In the C-terminal section; belongs to the carbohydrate kinase PfkB family.