The content of legal bills is very important to protect. We have technical safeguards as well as management/process safeguards. The most important of which is limiting the number of people with access to actual content.
We have data and can price compare across geographies and law firms. But it is important to remember that each transaction is unique. That's why we don't release any of that information currently. If we find the right way and the right venue to share that aggregated information, we will do so if we think it is in the best interest of our customers.
Separate issue whether disclosure of the bill to you as vendor, with a documented expectation of confidentiality, would constitute waiver either of WP or A/C privilege. No obvious reason that disclosure to your service would be different than disclosure to TyMetrix, Serengeti, or Sky Analytics, assuming your T&Cs are well-crafted. But obviously check with your lawyers on that.
Also, purely from a business standpoint, you can bet that some lawyers will raise the confidentiality objection to discourage/resist adoption.
All is to say, the issue is an important one. Glad to see you're taking it seriously. Good luck!
On the other side, your firm has placed itself in the unique position of being able to price-compare different law firms, and even different customers of the same firm. You could pivot/expand into a price-shopping service (kayak for law firms), a law-firm analytics provider (giving a/b testing results and other demographic info to law firms, leading to better price stratifying), or a service for law firms to gain pricing information about their competitors.