It's pretty easy to use venmo without giving them your banking information. That's how I've been using it for years. You just have to be willing to carry a balance. What I did is went to a coworker who has venmo and gave him $50 in cash, and in return he transferred $50 to my venmo.

That wouldn't work so well if you were always receiving money or always sending it, but if you have a pretty even mix then it works great.