Maybe. I wouldn't know for certain, because I am not a lawyer. But my understanding from working in this industry for a number of years is that under most state money transmitter laws customer funds are held in trust, meaning that in bankruptcy they are not actually company assets that can be assigned to debtors. Customers would have to be paid first.
In addition, it is very unlikely that the company would be allowed to go into bankruptcy. Right now, the company has ~$1 billion in cash of its own, net of debt, above and beyond customer funds. They can afford to take some losses as they continue to grow. Arguably, they should spend this capital on growth. Isn't this why they raised the money in the first place? Isn't it what their investors expect?
If their cash reserves diminish to the point where they cannot sustain or justify those losses, banking regulators will shut them down before dipping into customer funds even becomes a temptation.
Bill payment companies have existed for decades under this same regulatory scheme. Interest on float is an essential aspect of bill payment companies' profitability; for some companies, it exceeds their fee income. There is nothing that Bill.com is doing here that is not standard for the industry, and regulators know what to look for (after being burned in the past). If Bill.com went south in the way that you seem to be worried about, it would be a major scandal.