Does this booking platform exist?

Hi there! I work at a University where we host a few conferences in the spring across the States. We send groups of teachers & students to the conferences and are hoping to streamline efforts this year.

Does a platform like this exist? We'd like to invite them to the platform, where they can book their own travel, but we have a limit on their spending, and it charges us. So we could tell a teacher, you get $2000 for flights, here is the link to book from and it would only let them spend up to that much.