Plenty of people give their financial data to other businesses. I assume you keep money in the bank. You must trust them. Most banks, at least the larger ones offer online banking, which many people use all the time. PayPal seems pretty well used and they connect directly to your bank account so you can transfer money back and forth. And I mentioned Mint above which people trust with all of their personal financial information.

You may not trust companies over the internet. It's certainly you're right not to, but many people already do and many more people are trusting them everyday. Naturally the company needs to earn your trust. You wouldn't give the information over to just anyone. Again though you trust your bank. Why? They must have done something to earn your trust. Online companies can also earn a person or businesses trust.