He's on the appointments committee at his school and says "most of the clinical professors whose work we have reviewed this semester have pursued a model of inculcating left-liberal political values in students and deploying those students to advance left-liberal political causes."
Only most? Not all? Who were the ones who didn't? What are the forces that cause the applicants for this type of legal academic work to lean left? The "regular" professors tend to lean left as well, so it's only a question of degree, but clinical lawprof work tends to pay a lot less and to involve less pleasurable tasks than classic lawprof work.
Bainbridge's law school is UCLA. Here's a list of their clinics, including some that don't seem too lefty, like the Business Deals Clinic and Mergers & Acquisitions. But, realistically, you can see why someone with expertise practicing law in business deals mergers & acquisitions — the kind that would impress a law school appointments committee — has an incentive to stay in practice and not to shift into clinical teaching. The standard lawprof job has its obvious rewards, but why clinical teaching?
The system is founded on the reward the accrues to those with the left-liberal political agenda that Bainbridge rails against. It's baked into the cake.