I think it should be working on his project

It's true that the original text has an apparent typo (mistake). We wouldn't say "working on in his senior project," but we would say "working on his senior project." The text is offering a few different reasons or arguments as to why it's better to request a room on campus in this situation. One of the reasons offered is that commuting to campus by bus is time-consuming, and that isn't a good use of time during the period when this person needs to be making progress toward completion of his senior project. So during those months, he is "working on" his project - he is continuously, probably every day, several hours per week, performing work to complete parts of this project, and he has a goal of ultimately completing the project. And he needs his study time to do this - he doesn't want to spend it needlessly commuting!