I don't think making it free is a good idea, because people have no respect for something provided for free, so you'll end up making the service more expensive

I don't think making it free is a good idea, because people have no respect for something provided for free, so you'll end up making the service more expensive to maintain and at a lower quality than by charging a nominal amount. However, you can use pricing to discourage paying to the driver. Where I live (belgium) I can pay 2 euro per ride to the driver, or 80 euro for unlimited travel during a whole year (partially subsidized by my employer, which they're legally required to do), or any of a range of payment options in between. Paying cash to the driver is so much more expensive than the alternatives that almost nobody does it.