I was turned away because I don't have a business checking account. It's not reasonable to expect an Uber/Lyft driver to have a business account.
I think you're wrong. Many people believe owning a business means you run a corporation, you own a store, or something along those lines. However, you are also technically a business owner if you’re in a solo profession. Freelance writers, rideshare drivers, and artists are also business owners, and opening a business bank account can do wonders for you.
If your organization has an Uber for Business account, you can use your Uber rider app to take rides and have them billed directly to your company. Your ride experience is the same for both your personal and Uber for Business profiles – you can toggle between them for personal and business trips
You were turned away from your bank or you were turned away from Uber/Lyft? Either way, you don't need a business account but since you are a driver and an independent contractor you are technically a business owner by way of your own services. You are the business.
I am not sure I am understanding the question right. You need to have a driver account to drive for Uber and Lyft otherwise you will not have access to people looking for rides. If that is what you are asking?