For most fintech founders, getting a bank to buy your software is the holy grail.

But Caroline Plumb, chief executive of Fluidly, an artificial intelligence-driven start-up that helps companies with cash flow management, is not in that camp. In fact, she is positively wary of collaborating with banks, which can be skittish about commitments. “The danger of working with banks is that you could have wasted your time,” she said.